#include <darcy_elements.h>

Inheritance diagram for oomph::DarcyEquations< DIM >:

Public Types
typedef void(*	SourceFctPt) (const Vector< double > &x, Vector< double > &f)
	Source function pointer typedef. More...

typedef void(*	MassSourceFctPt) (const Vector< double > &x, double &f)
	Mass source function pointer typedef. More...

Public Types inherited from oomph::FiniteElement
typedef void(*	SteadyExactSolutionFctPt) (const Vector< double > &, Vector< double > &)

typedef void(*	UnsteadyExactSolutionFctPt) (const double &, const Vector< double > &, Vector< double > &)

Public Member Functions
	DarcyEquations ()
	Constructor. More...

SourceFctPt &	source_fct_pt ()
	Access function: Pointer to body force function. More...

SourceFctPt	source_fct_pt () const
	Access function: Pointer to body force function (const version) More...

MassSourceFctPt &	mass_source_fct_pt ()
	Access function: Pointer to mass source function. More...

MassSourceFctPt	mass_source_fct_pt () const
	Access function: Pointer to mass source function (const version) More...

void	source (const Vector< double > &x, Vector< double > &b) const

void	mass_source (const Vector< double > &x, double &b) const

virtual unsigned	required_nvalue (const unsigned &n) const =0
	Number of values required at node n. More...

virtual int	q_edge_local_eqn (const unsigned &n) const =0
	Return the equation number of the n-th edge (flux) degree of freedom. More...

virtual int	q_internal_local_eqn (const unsigned &n) const =0
	Return the equation number of the n-th internal degree of freedom. More...

virtual Vector< Data * >	q_edge_data_pt () const =0

virtual Data *	q_internal_data_pt () const =0
	Return pointer to the Data object that stores the internal flux values. More...

virtual unsigned	q_edge_index (const unsigned &n) const =0
	Return the nodal index at which the nth edge unknown is stored. More...

virtual unsigned	q_internal_index () const =0

virtual unsigned	q_edge_node_number (const unsigned &n) const =0
	Return the number of the node where the nth edge unknown is stored. More...

virtual double	q_edge (const unsigned &n) const =0
	Return the values of the n-th edge (flux) degree of freedom. More...

virtual unsigned	face_index_of_q_edge_basis_fct (const unsigned &j) const =0
	Return the face index associated with edge flux degree of freedom. More...

virtual unsigned	face_index_of_edge (const unsigned &j) const =0
	Return the face index associated with specified edge. More...

virtual void	face_local_coordinate_of_flux_interpolation_point (const unsigned &edge, const unsigned &n, Vector< double > &s) const =0

virtual double	q_internal (const unsigned &n) const =0
	Return the values of the internal degree of freedom. More...

virtual void	set_q_edge (const unsigned &n, const double &value)=0
	Set the values of the edge (flux) degree of freedom. More...

virtual void	set_q_internal (const unsigned &n, const double &value)=0
	Set the values of the internal degree of freedom. More...

unsigned	nq_basis () const
	Return the total number of computational basis functions for q. More...

virtual unsigned	nq_basis_edge () const =0
	Return the number of edge basis functions for q. More...

virtual unsigned	nq_basis_internal () const =0
	Return the number of internal basis functions for q. More...

virtual void	get_q_basis_local (const Vector< double > &s, Shape &q_basis) const =0
	Returns the local form of the q basis at local coordinate s. More...

virtual void	get_div_q_basis_local (const Vector< double > &s, Shape &div_q_basis_ds) const =0

void	get_q_basis (const Vector< double > &s, Shape &q_basis) const
	Returns the transformed basis at local coordinate s. More...

virtual unsigned	nedge_flux_interpolation_point () const =0

virtual void	edge_flux_interpolation_point_global (const unsigned &j, Vector< double > &x) const =0

virtual Vector< double >	edge_flux_interpolation_point (const unsigned &edge, const unsigned &n) const =0

virtual void	edge_flux_interpolation_point_global (const unsigned &edge, const unsigned &n, Vector< double > &x) const =0

virtual void	pin_q_internal_value (const unsigned &n)=0
	Pin the nth internal q value. More...

virtual int	p_local_eqn (const unsigned &n) const =0
	Return the equation number of the n-th pressure degree of freedom. More...

virtual double	p_value (const unsigned &n) const =0
	Return the nth pressure value. More...

virtual unsigned	np_basis () const =0
	Return the total number of pressure basis functions. More...

virtual void	get_p_basis (const Vector< double > &s, Shape &p_basis) const =0
	Return the pressure basis. More...

virtual void	pin_p_value (const unsigned &n)=0
	Pin the nth pressure value. More...

virtual void	set_p_value (const unsigned &n, const double &value)=0
	Set the nth pressure value. More...

virtual Data *	p_data_pt () const =0
	Return pointer to the Data object that stores the pressure values. More...

virtual void	scale_basis (Shape &basis) const =0
	Scale the edge basis to allow arbitrary edge mappings. More...

double	transform_basis (const Vector< double > &s, const Shape &q_basis_local, Shape &psi, Shape &q_basis) const

void	fill_in_contribution_to_residuals (Vector< double > &residuals)
	Fill in contribution to residuals for the Darcy equations. More...

void	interpolated_q (const Vector< double > &s, Vector< double > &q) const
	Calculate the FE representation of q. More...

double	interpolated_q (const Vector< double > &s, const unsigned i) const
	Calculate the FE representation of the i-th component of q. More...

void	interpolated_div_q (const Vector< double > &s, double &div_q) const
	Calculate the FE representation of div q. More...

double	interpolated_div_q (const Vector< double > &s)
	Calculate the FE representation of div q and return it. More...

void	interpolated_p (const Vector< double > &s, double &p) const
	Calculate the FE representation of p. More...

double	interpolated_p (const Vector< double > &s) const
	Calculate the FE representation of p and return it. More...

virtual void	pin_superfluous_darcy_dofs ()

unsigned	self_test ()
	Self test – empty for now. More...

void	output (std::ostream &outfile)
	Output with default number of plot points. More...

void	output (std::ostream &outfile, const unsigned &nplot)

void	output_with_projected_flux (std::ostream &outfile, const unsigned &nplot, const Vector< double > unit_normal)
	Output FE representation of soln: x,y,q1,q2,div_q,p,q \cdot n. More...

void	output_fct (std::ostream &outfile, const unsigned &nplot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)

void	compute_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, Vector< double > &error, Vector< double > &norm)

unsigned	num_Z2_flux_terms ()
	Number off flux terms for Z2 error estimator (use actual flux) More...

void	get_Z2_flux (const Vector< double > &s, Vector< double > &flux)
	Z2 flux (use actual flux) More...

Public Member Functions inherited from oomph::FiniteElement
void	set_dimension (const unsigned &dim)

void	set_nodal_dimension (const unsigned &nodal_dim)

void	set_nnodal_position_type (const unsigned &nposition_type)
	Set the number of types required to interpolate the coordinate. More...

void	set_n_node (const unsigned &n)

int	nodal_local_eqn (const unsigned &n, const unsigned &i) const

double	dJ_eulerian_at_knot (const unsigned &ipt, Shape &psi, DenseMatrix< double > &djacobian_dX) const

	FiniteElement ()
	Constructor. More...

virtual	~FiniteElement ()

	FiniteElement (const FiniteElement &)=delete
	Broken copy constructor. More...

virtual bool	local_coord_is_valid (const Vector< double > &s)
	Broken assignment operator. More...

virtual void	move_local_coord_back_into_element (Vector< double > &s) const

void	get_centre_of_gravity_and_max_radius_in_terms_of_zeta (Vector< double > &cog, double &max_radius) const

virtual void	local_coordinate_of_node (const unsigned &j, Vector< double > &s) const

virtual void	local_fraction_of_node (const unsigned &j, Vector< double > &s_fraction)

virtual double	local_one_d_fraction_of_node (const unsigned &n1d, const unsigned &i)

virtual void	set_macro_elem_pt (MacroElement *macro_elem_pt)

MacroElement *	macro_elem_pt ()
	Access function to pointer to macro element. More...

void	get_x (const Vector< double > &s, Vector< double > &x) const

void	get_x (const unsigned &t, const Vector< double > &s, Vector< double > &x)

virtual void	get_x_from_macro_element (const Vector< double > &s, Vector< double > &x) const

virtual void	get_x_from_macro_element (const unsigned &t, const Vector< double > &s, Vector< double > &x)

virtual void	set_integration_scheme (Integral *const &integral_pt)
	Set the spatial integration scheme. More...

Integral *const &	integral_pt () const
	Return the pointer to the integration scheme (const version) More...

virtual void	shape (const Vector< double > &s, Shape &psi) const =0

virtual void	shape_at_knot (const unsigned &ipt, Shape &psi) const

virtual void	dshape_local (const Vector< double > &s, Shape &psi, DShape &dpsids) const

virtual void	dshape_local_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsids) const

virtual void	d2shape_local (const Vector< double > &s, Shape &psi, DShape &dpsids, DShape &d2psids) const

virtual void	d2shape_local_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsids, DShape &d2psids) const

virtual double	J_eulerian (const Vector< double > &s) const

virtual double	J_eulerian_at_knot (const unsigned &ipt) const

void	check_J_eulerian_at_knots (bool &passed) const

void	check_jacobian (const double &jacobian) const

double	dshape_eulerian (const Vector< double > &s, Shape &psi, DShape &dpsidx) const

virtual double	dshape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidx) const

virtual double	dshape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsi, DenseMatrix< double > &djacobian_dX, RankFourTensor< double > &d_dpsidx_dX) const

double	d2shape_eulerian (const Vector< double > &s, Shape &psi, DShape &dpsidx, DShape &d2psidx) const

virtual double	d2shape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidx, DShape &d2psidx) const

virtual void	assign_nodal_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	describe_local_dofs (std::ostream &out, const std::string &current_string) const

virtual void	describe_nodal_local_dofs (std::ostream &out, const std::string &current_string) const

virtual void	assign_all_generic_local_eqn_numbers (const bool &store_local_dof_pt)

Node *&	node_pt (const unsigned &n)
	Return a pointer to the local node n. More...

Node *const &	node_pt (const unsigned &n) const
	Return a pointer to the local node n (const version) More...

unsigned	nnode () const
	Return the number of nodes. More...

virtual unsigned	nnode_1d () const

double	raw_nodal_position (const unsigned &n, const unsigned &i) const

double	raw_nodal_position (const unsigned &t, const unsigned &n, const unsigned &i) const

double	raw_dnodal_position_dt (const unsigned &n, const unsigned &i) const

double	raw_dnodal_position_dt (const unsigned &n, const unsigned &j, const unsigned &i) const

double	raw_nodal_position_gen (const unsigned &n, const unsigned &k, const unsigned &i) const

double	raw_nodal_position_gen (const unsigned &t, const unsigned &n, const unsigned &k, const unsigned &i) const

double	raw_dnodal_position_gen_dt (const unsigned &n, const unsigned &k, const unsigned &i) const

double	raw_dnodal_position_gen_dt (const unsigned &j, const unsigned &n, const unsigned &k, const unsigned &i) const

double	nodal_position (const unsigned &n, const unsigned &i) const

double	nodal_position (const unsigned &t, const unsigned &n, const unsigned &i) const

double	dnodal_position_dt (const unsigned &n, const unsigned &i) const
	Return the i-th component of nodal velocity: dx/dt at local node n. More...

double	dnodal_position_dt (const unsigned &n, const unsigned &j, const unsigned &i) const

double	nodal_position_gen (const unsigned &n, const unsigned &k, const unsigned &i) const

double	nodal_position_gen (const unsigned &t, const unsigned &n, const unsigned &k, const unsigned &i) const

double	dnodal_position_gen_dt (const unsigned &n, const unsigned &k, const unsigned &i) const

double	dnodal_position_gen_dt (const unsigned &j, const unsigned &n, const unsigned &k, const unsigned &i) const

virtual void	get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates)

virtual void	disable_ALE ()

virtual void	enable_ALE ()

unsigned	nnodal_position_type () const

bool	has_hanging_nodes () const

unsigned	nodal_dimension () const
	Return the required Eulerian dimension of the nodes in this element. More...

virtual Node *	construct_node (const unsigned &n)

virtual Node *	construct_node (const unsigned &n, TimeStepper *const &time_stepper_pt)

virtual Node *	construct_boundary_node (const unsigned &n)

virtual Node *	construct_boundary_node (const unsigned &n, TimeStepper *const &time_stepper_pt)

int	get_node_number (Node *const &node_pt) const

virtual Node *	get_node_at_local_coordinate (const Vector< double > &s) const

double	raw_nodal_value (const unsigned &n, const unsigned &i) const

double	raw_nodal_value (const unsigned &t, const unsigned &n, const unsigned &i) const

double	nodal_value (const unsigned &n, const unsigned &i) const

double	nodal_value (const unsigned &t, const unsigned &n, const unsigned &i) const

unsigned	dim () const

virtual ElementGeometry::ElementGeometry	element_geometry () const
	Return the geometry type of the element (either Q or T usually). More...

virtual double	interpolated_x (const Vector< double > &s, const unsigned &i) const
	Return FE interpolated coordinate x[i] at local coordinate s. More...

virtual double	interpolated_x (const unsigned &t, const Vector< double > &s, const unsigned &i) const

virtual void	interpolated_x (const Vector< double > &s, Vector< double > &x) const
	Return FE interpolated position x[] at local coordinate s as Vector. More...

virtual void	interpolated_x (const unsigned &t, const Vector< double > &s, Vector< double > &x) const

virtual double	interpolated_dxdt (const Vector< double > &s, const unsigned &i, const unsigned &t)

virtual void	interpolated_dxdt (const Vector< double > &s, const unsigned &t, Vector< double > &dxdt)

unsigned	ngeom_data () const

Data *	geom_data_pt (const unsigned &j)

void	position (const Vector< double > &zeta, Vector< double > &r) const

void	position (const unsigned &t, const Vector< double > &zeta, Vector< double > &r) const

void	dposition_dt (const Vector< double > &zeta, const unsigned &t, Vector< double > &drdt)

virtual double	zeta_nodal (const unsigned &n, const unsigned &k, const unsigned &i) const

void	interpolated_zeta (const Vector< double > &s, Vector< double > &zeta) const

void	locate_zeta (const Vector< double > &zeta, GeomObject *&geom_object_pt, Vector< double > &s, const bool &use_coordinate_as_initial_guess=false)

virtual void	node_update ()

virtual void	identify_field_data_for_interactions (std::set< std::pair< Data *, unsigned >> &paired_field_data)

virtual void	identify_geometric_data (std::set< Data * > &geometric_data_pt)

virtual double	s_min () const
	Min value of local coordinate. More...

virtual double	s_max () const
	Max. value of local coordinate. More...

double	size () const

virtual double	compute_physical_size () const

virtual void	point_output_data (const Vector< double > &s, Vector< double > &data)

void	point_output (std::ostream &outfile, const Vector< double > &s)

virtual unsigned	nplot_points_paraview (const unsigned &nplot) const

virtual unsigned	nsub_elements_paraview (const unsigned &nplot) const

void	output_paraview (std::ofstream &file_out, const unsigned &nplot) const

virtual void	write_paraview_output_offset_information (std::ofstream &file_out, const unsigned &nplot, unsigned &counter) const

virtual void	write_paraview_type (std::ofstream &file_out, const unsigned &nplot) const

virtual void	write_paraview_offsets (std::ofstream &file_out, const unsigned &nplot, unsigned &offset_sum) const

virtual unsigned	nscalar_paraview () const

virtual void	scalar_value_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot) const

virtual void	scalar_value_fct_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt) const

virtual void	scalar_value_fct_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot, const double &time, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt) const

virtual std::string	scalar_name_paraview (const unsigned &i) const

virtual void	output (const unsigned &t, std::ostream &outfile, const unsigned &n_plot) const

virtual void	output (FILE *file_pt)

virtual void	output (FILE *file_pt, const unsigned &n_plot)

virtual void	output_fct (std::ostream &outfile, const unsigned &n_plot, const double &time, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt)
	Output a time-dependent exact solution over the element. More...

virtual void	output_fct (std::ostream &outfile, const unsigned &n_plot, const double &time, const SolutionFunctorBase &exact_soln) const
	Output a time-dependent exact solution over the element. More...

virtual void	get_s_plot (const unsigned &i, const unsigned &nplot, Vector< double > &s, const bool &shifted_to_interior=false) const

virtual std::string	tecplot_zone_string (const unsigned &nplot) const

virtual void	write_tecplot_zone_footer (std::ostream &outfile, const unsigned &nplot) const

virtual void	write_tecplot_zone_footer (FILE *file_pt, const unsigned &nplot) const

virtual unsigned	nplot_points (const unsigned &nplot) const

virtual void	compute_error (FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)
	Calculate the norm of the error and that of the exact solution. More...

virtual void	compute_error (FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, double &norm)
	Calculate the norm of the error and that of the exact solution. More...

virtual void	compute_error (FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, Vector< double > &error, Vector< double > &norm)

virtual void	compute_error (FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, Vector< double > &error, Vector< double > &norm)

virtual void	compute_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)

virtual void	compute_error (std::ostream &outfile, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, double &norm)

virtual void	compute_error (std::ostream &outfile, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, Vector< double > &error, Vector< double > &norm)

virtual void	compute_abs_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error)

void	integrate_fct (FiniteElement::SteadyExactSolutionFctPt integrand_fct_pt, Vector< double > &integral)
	Integrate Vector-valued function over element. More...

void	integrate_fct (FiniteElement::UnsteadyExactSolutionFctPt integrand_fct_pt, const double &time, Vector< double > &integral)
	Integrate Vector-valued time-dep function over element. More...

virtual void	build_face_element (const int &face_index, FaceElement *face_element_pt)

virtual unsigned	get_bulk_node_number (const int &face_index, const unsigned &i) const

virtual int	face_outer_unit_normal_sign (const int &face_index) const
	Get the sign of the outer unit normal on the face given by face_index. More...

virtual unsigned	nnode_on_face () const

void	face_node_number_error_check (const unsigned &i) const
	Range check for face node numbers. More...

virtual CoordinateMappingFctPt	face_to_bulk_coordinate_fct_pt (const int &face_index) const

virtual BulkCoordinateDerivativesFctPt	bulk_coordinate_derivatives_fct_pt (const int &face_index) const

Public Member Functions inherited from oomph::GeneralisedElement
	GeneralisedElement ()
	Constructor: Initialise all pointers and all values to zero. More...

virtual	~GeneralisedElement ()
	Virtual destructor to clean up any memory allocated by the object. More...

	GeneralisedElement (const GeneralisedElement &)=delete
	Broken copy constructor. More...

void	operator= (const GeneralisedElement &)=delete
	Broken assignment operator. More...

Data *&	internal_data_pt (const unsigned &i)
	Return a pointer to i-th internal data object. More...

Data *const &	internal_data_pt (const unsigned &i) const
	Return a pointer to i-th internal data object (const version) More...

Data *&	external_data_pt (const unsigned &i)
	Return a pointer to i-th external data object. More...

Data *const &	external_data_pt (const unsigned &i) const
	Return a pointer to i-th external data object (const version) More...

unsigned long	eqn_number (const unsigned &ieqn_local) const

int	local_eqn_number (const unsigned long &ieqn_global) const

unsigned	add_external_data (Data *const &data_pt, const bool &fd=true)

bool	external_data_fd (const unsigned &i) const

void	exclude_external_data_fd (const unsigned &i)

void	include_external_data_fd (const unsigned &i)

void	flush_external_data ()
	Flush all external data. More...

void	flush_external_data (Data *const &data_pt)
	Flush the object addressed by data_pt from the external data array. More...

unsigned	ninternal_data () const
	Return the number of internal data objects. More...

unsigned	nexternal_data () const
	Return the number of external data objects. More...

unsigned	ndof () const
	Return the number of equations/dofs in the element. More...

void	dof_vector (const unsigned &t, Vector< double > &dof)
	Return the vector of dof values at time level t. More...

void	dof_pt_vector (Vector< double * > &dof_pt)
	Return the vector of pointers to dof values. More...

void	set_internal_data_time_stepper (const unsigned &i, TimeStepper *const &time_stepper_pt, const bool &preserve_existing_data)

void	assign_internal_eqn_numbers (unsigned long &global_number, Vector< double * > &Dof_pt)

void	describe_dofs (std::ostream &out, const std::string &current_string) const

void	add_internal_value_pt_to_map (std::map< unsigned, double * > &map_of_value_pt)

virtual void	assign_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	complete_setup_of_dependencies ()

virtual void	get_residuals (Vector< double > &residuals)

virtual void	get_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)

virtual void	get_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &mass_matrix)

virtual void	get_jacobian_and_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix)

virtual void	get_dresiduals_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam)

virtual void	get_djacobian_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam)

virtual void	get_djacobian_and_dmass_matrix_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam, DenseMatrix< double > &dmass_matrix_dparam)

virtual void	get_hessian_vector_products (Vector< double > const &Y, DenseMatrix< double > const &C, DenseMatrix< double > &product)

virtual void	get_inner_products (Vector< std::pair< unsigned, unsigned >> const &history_index, Vector< double > &inner_product)

virtual void	get_inner_product_vectors (Vector< unsigned > const &history_index, Vector< Vector< double >> &inner_product_vector)

virtual void	compute_norm (Vector< double > &norm)

virtual void	compute_norm (double &norm)

virtual unsigned	ndof_types () const

virtual void	get_dof_numbers_for_unknowns (std::list< std::pair< unsigned long, unsigned >> &dof_lookup_list) const

Public Member Functions inherited from oomph::GeomObject
	GeomObject ()
	Default constructor. More...

	GeomObject (const unsigned &ndim)

	GeomObject (const unsigned &nlagrangian, const unsigned &ndim)

	GeomObject (const unsigned &nlagrangian, const unsigned &ndim, TimeStepper *time_stepper_pt)

	GeomObject (const GeomObject &dummy)=delete
	Broken copy constructor. More...

void	operator= (const GeomObject &)=delete
	Broken assignment operator. More...

virtual	~GeomObject ()
	(Empty) destructor More...

unsigned	nlagrangian () const
	Access function to # of Lagrangian coordinates. More...

unsigned	ndim () const
	Access function to # of Eulerian coordinates. More...

void	set_nlagrangian_and_ndim (const unsigned &n_lagrangian, const unsigned &n_dim)
	Set # of Lagrangian and Eulerian coordinates. More...

TimeStepper *&	time_stepper_pt ()

TimeStepper *	time_stepper_pt () const

virtual void	position (const double &t, const Vector< double > &zeta, Vector< double > &r) const

virtual void	dposition (const Vector< double > &zeta, DenseMatrix< double > &drdzeta) const

virtual void	d2position (const Vector< double > &zeta, RankThreeTensor< double > &ddrdzeta) const

virtual void	d2position (const Vector< double > &zeta, Vector< double > &r, DenseMatrix< double > &drdzeta, RankThreeTensor< double > &ddrdzeta) const

Public Member Functions inherited from oomph::ElementWithZ2ErrorEstimator
	ElementWithZ2ErrorEstimator ()
	Default empty constructor. More...

	ElementWithZ2ErrorEstimator (const ElementWithZ2ErrorEstimator &)=delete
	Broken copy constructor. More...

void	operator= (const ElementWithZ2ErrorEstimator &)=delete
	Broken assignment operator. More...

virtual unsigned	ncompound_fluxes ()

virtual void	compute_exact_Z2_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_flux_pt, double &error, double &norm)

virtual void	get_Z2_compound_flux_indices (Vector< unsigned > &flux_index)

virtual unsigned	nvertex_node () const =0
	Number of vertex nodes in the element. More...

virtual Node *	vertex_node_pt (const unsigned &j) const =0

virtual unsigned	nrecovery_order ()=0
	Order of recovery shape functions. More...

virtual double	geometric_jacobian (const Vector< double > &x)

Protected Member Functions
virtual double	shape_basis_test_local (const Vector< double > &s, Shape &psi, Shape &q_basis, Shape &q_test, Shape &p_basis, Shape &p_test, Shape &div_q_basis_ds, Shape &div_q_test_ds) const =0

virtual double	shape_basis_test_local_at_knot (const unsigned &ipt, Shape &psi, Shape &q_basis, Shape &q_test, Shape &p_basis, Shape &p_test, Shape &div_q_basis_ds, Shape &div_q_test_ds) const =0

virtual void	fill_in_generic_residual_contribution (Vector< double > &residuals, DenseMatrix< double > &jacobian, bool flag)
	Fill in residuals and, if flag==true, jacobian. More...

Protected Member Functions inherited from oomph::FiniteElement
virtual void	assemble_local_to_eulerian_jacobian (const DShape &dpsids, DenseMatrix< double > &jacobian) const

virtual void	assemble_local_to_eulerian_jacobian2 (const DShape &d2psids, DenseMatrix< double > &jacobian2) const

virtual void	assemble_eulerian_base_vectors (const DShape &dpsids, DenseMatrix< double > &interpolated_G) const

template<unsigned DIM>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const

virtual double	invert_jacobian_mapping (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const

virtual double	local_to_eulerian_mapping (const DShape &dpsids, DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const

double	local_to_eulerian_mapping (const DShape &dpsids, DenseMatrix< double > &inverse_jacobian) const

virtual double	local_to_eulerian_mapping_diagonal (const DShape &dpsids, DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const

virtual void	dJ_eulerian_dnodal_coordinates (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const

template<unsigned DIM>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const

virtual void	d_dshape_eulerian_dnodal_coordinates (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const

template<unsigned DIM>
void	d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const

virtual void	transform_derivatives (const DenseMatrix< double > &inverse_jacobian, DShape &dbasis) const

void	transform_derivatives_diagonal (const DenseMatrix< double > &inverse_jacobian, DShape &dbasis) const

virtual void	transform_second_derivatives (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const

template<unsigned DIM>
void	transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const

template<unsigned DIM>
void	transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const

virtual void	fill_in_jacobian_from_nodal_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian)

void	fill_in_jacobian_from_nodal_by_fd (DenseMatrix< double > &jacobian)

virtual void	update_before_nodal_fd ()

virtual void	reset_after_nodal_fd ()

virtual void	update_in_nodal_fd (const unsigned &i)

virtual void	reset_in_nodal_fd (const unsigned &i)

void	fill_in_contribution_to_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)

template<>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	Zero-d specialisation of function to calculate inverse of jacobian mapping. More...

template<>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	One-d specialisation of function to calculate inverse of jacobian mapping. More...

template<>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	Two-d specialisation of function to calculate inverse of jacobian mapping. More...

template<>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const

template<>
void	d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const

template<>
void	d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const

template<>
void	d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const

template<>
void	d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const

template<>
void	transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const

template<>
void	transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const

template<>
void	transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const

template<>
void	transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const

Protected Member Functions inherited from oomph::GeneralisedElement
unsigned	add_internal_data (Data *const &data_pt, const bool &fd=true)

bool	internal_data_fd (const unsigned &i) const

void	exclude_internal_data_fd (const unsigned &i)

void	include_internal_data_fd (const unsigned &i)

void	clear_global_eqn_numbers ()

void	add_global_eqn_numbers (std::deque< unsigned long > const &global_eqn_numbers, std::deque< double * > const &global_dof_pt)

virtual void	assign_internal_and_external_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	assign_additional_local_eqn_numbers ()

int	internal_local_eqn (const unsigned &i, const unsigned &j) const

int	external_local_eqn (const unsigned &i, const unsigned &j)

void	fill_in_jacobian_from_internal_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian, const bool &fd_all_data=false)

void	fill_in_jacobian_from_internal_by_fd (DenseMatrix< double > &jacobian, const bool &fd_all_data=false)

void	fill_in_jacobian_from_external_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian, const bool &fd_all_data=false)

void	fill_in_jacobian_from_external_by_fd (DenseMatrix< double > &jacobian, const bool &fd_all_data=false)

virtual void	update_before_internal_fd ()

virtual void	reset_after_internal_fd ()

virtual void	update_in_internal_fd (const unsigned &i)

virtual void	reset_in_internal_fd (const unsigned &i)

virtual void	update_before_external_fd ()

virtual void	reset_after_external_fd ()

virtual void	update_in_external_fd (const unsigned &i)

virtual void	reset_in_external_fd (const unsigned &i)

virtual void	fill_in_contribution_to_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &mass_matrix)

virtual void	fill_in_contribution_to_jacobian_and_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix)

virtual void	fill_in_contribution_to_dresiduals_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam)

virtual void	fill_in_contribution_to_djacobian_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam)

virtual void	fill_in_contribution_to_djacobian_and_dmass_matrix_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam, DenseMatrix< double > &dmass_matrix_dparam)

virtual void	fill_in_contribution_to_hessian_vector_products (Vector< double > const &Y, DenseMatrix< double > const &C, DenseMatrix< double > &product)

virtual void	fill_in_contribution_to_inner_products (Vector< std::pair< unsigned, unsigned >> const &history_index, Vector< double > &inner_product)

virtual void	fill_in_contribution_to_inner_product_vectors (Vector< unsigned > const &history_index, Vector< Vector< double >> &inner_product_vector)

Private Attributes
SourceFctPt	Source_fct_pt
	Pointer to body force function. More...

MassSourceFctPt	Mass_source_fct_pt
	Pointer to the mass source function. More...

Additional Inherited Members
Static Public Attributes inherited from oomph::FiniteElement
static double	Tolerance_for_singular_jacobian = 1.0e-16
	Tolerance below which the jacobian is considered singular. More...

static bool	Accept_negative_jacobian = false

static bool	Suppress_output_while_checking_for_inverted_elements

Static Public Attributes inherited from oomph::GeneralisedElement
static bool	Suppress_warning_about_repeated_internal_data

static bool	Suppress_warning_about_repeated_external_data = true

static double	Default_fd_jacobian_step = 1.0e-8

Protected Attributes inherited from oomph::FiniteElement
MacroElement *	Macro_elem_pt
	Pointer to the element's macro element (NULL by default) More...

Protected Attributes inherited from oomph::GeomObject
unsigned	NLagrangian
	Number of Lagrangian (intrinsic) coordinates. More...

unsigned	Ndim
	Number of Eulerian coordinates. More...

TimeStepper *	Geom_object_time_stepper_pt

Static Protected Attributes inherited from oomph::FiniteElement
static const unsigned	Default_Initial_Nvalue = 0
	Default value for the number of values at a node. More...

static const double	Node_location_tolerance = 1.0e-14

static const unsigned	N2deriv [] = {0, 1, 3, 6}

Static Protected Attributes inherited from oomph::GeneralisedElement
static DenseMatrix< double >	Dummy_matrix

static std::deque< double * >	Dof_pt_deque

Detailed Description

template<unsigned DIM>
class oomph::DarcyEquations< DIM >

Class implementing the generic maths of the Darcy equations using Raviart-Thomas elements with both edge and internal degrees of freedom

Member Typedef Documentation

◆ MassSourceFctPt

template<unsigned DIM>

typedef void(* oomph::DarcyEquations< DIM >::MassSourceFctPt) (const Vector< double > &x, double &f)

Mass source function pointer typedef.

◆ SourceFctPt

template<unsigned DIM>

typedef void(* oomph::DarcyEquations< DIM >::SourceFctPt) (const Vector< double > &x, Vector< double > &f)

Source function pointer typedef.

Constructor & Destructor Documentation

◆ DarcyEquations()

template<unsigned DIM>

oomph::DarcyEquations< DIM >::DarcyEquations ( )

inline

Constructor.

58 : Source_fct_pt(0), Mass_source_fct_pt(0) {}

oomph::DarcyEquations::Mass_source_fct_pt

MassSourceFctPt Mass_source_fct_pt

Pointer to the mass source function.

Definition: darcy_elements.h:504

oomph::DarcyEquations::Source_fct_pt

SourceFctPt Source_fct_pt

Pointer to body force function.

Definition: darcy_elements.h:501

Member Function Documentation

◆ compute_error()

template<unsigned DIM>

void oomph::DarcyEquations< DIM >::compute_error	(	std::ostream &	outfile,
		FiniteElement::SteadyExactSolutionFctPt	exact_soln_pt,
		Vector< double > &	error,
		Vector< double > &	norm
	)

virtual

Compute the error between the FE solution and the exact solution using the H(div) norm for q and L^2 norm for p

Reimplemented from oomph::FiniteElement.

   {
     for (unsigned i = 0; i < 2; i++)
     {
       error[i] = 0.0;
       norm[i] = 0.0;
     }
  
     // Vector of local coordinates
     Vector<double> s(DIM);
  
     // Vector for coordinates
     Vector<double> x(DIM);
  
     // Set the value of n_intpt
     unsigned n_intpt = this->integral_pt()->nweight();
  
     outfile << "ZONE" << std::endl;
  
     // Exact solution Vector (u,v,[w])
     Vector<double> exact_soln(DIM + 2);
  
     // Loop over the integration points
     for (unsigned ipt = 0; ipt < n_intpt; ipt++)
     {
       // Assign values of s
       for (unsigned i = 0; i < DIM; i++)
       {
         s[i] = this->integral_pt()->knot(ipt, i);
       }
  
       // Get the integral weight
       double w = this->integral_pt()->weight(ipt);
  
       // Get jacobian of mapping
       double J = this->J_eulerian(s);
  
       // Premultiply the weights and the Jacobian
       double W = w * J;
  
       // Get x position as Vector
       this->interpolated_x(s, x);
  
       // Get exact solution at this point
       (*exact_soln_pt)(x, exact_soln);
  
       // Flux error
       for (unsigned i = 0; i < DIM; i++)
       {
         norm[0] += exact_soln[i] * exact_soln[i] * W;
         // Error due to q_i
         error[0] += (exact_soln[i] - this->interpolated_q(s, i)) *
                     (exact_soln[i] - this->interpolated_q(s, i)) * W;
       }
  
       // // Flux divergence error
       // norm[0]+=exact_soln[DIM]*exact_soln[DIM]*W;
       // error[0]+=(exact_soln[DIM]-interpolated_div_q(s))*
       //           (exact_soln[DIM]-interpolated_div_q(s))*W;
  
       // Pressure error
       norm[1] += exact_soln[DIM + 1] * exact_soln[DIM + 1] * W;
       error[1] += (exact_soln[DIM + 1] - this->interpolated_p(s)) *
                   (exact_soln[DIM + 1] - this->interpolated_p(s)) * W;
  
       // Output x,y,[z]
       for (unsigned i = 0; i < DIM; i++)
       {
         outfile << x[i] << " ";
       }
  
       // Output q_1_error,q_2_error,...
       for (unsigned i = 0; i < DIM; i++)
       {
         outfile << exact_soln[i] - this->interpolated_q(s, i) << " ";
       }
  
       // Output p_error
       outfile << exact_soln[DIM + 1] - this->interpolated_p(s) << " ";
  
       outfile << std::endl;
     }
   }

References DIM, calibrate::error, ProblemParameters::exact_soln(), i, J, s, w, oomph::QuadTreeNames::W, and plotDoE::x.

◆ edge_flux_interpolation_point()

template<unsigned DIM>

virtual Vector<double> oomph::DarcyEquations< DIM >::edge_flux_interpolation_point	(	const unsigned &	edge,
		const unsigned &	n
	)		const

pure virtual

Returns the local coordinate of nth flux interpolation point along an edge

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >.

◆ edge_flux_interpolation_point_global() [1/2]

template<unsigned DIM>

virtual void oomph::DarcyEquations< DIM >::edge_flux_interpolation_point_global	(	const unsigned &	edge,
		const unsigned &	n,
		Vector< double > &	x
	)		const

pure virtual

Returns the global coordinates of the nth flux interpolation point along an edge

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >.

◆ edge_flux_interpolation_point_global() [2/2]

template<unsigned DIM>

virtual void oomph::DarcyEquations< DIM >::edge_flux_interpolation_point_global	(	const unsigned &	j,
		Vector< double > &	x
	)		const

pure virtual

Compute the global coordinates of the flux_interpolation point associated with the j-th edge-based q basis fct

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >.

◆ face_index_of_edge()

template<unsigned DIM>

virtual unsigned oomph::DarcyEquations< DIM >::face_index_of_edge ( const unsigned & j ) const

pure virtual

Return the face index associated with specified edge.

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >.

◆ face_index_of_q_edge_basis_fct()

template<unsigned DIM>

virtual unsigned oomph::DarcyEquations< DIM >::face_index_of_q_edge_basis_fct ( const unsigned & j ) const

pure virtual

Return the face index associated with edge flux degree of freedom.

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >.

◆ face_local_coordinate_of_flux_interpolation_point()

template<unsigned DIM>

virtual void oomph::DarcyEquations< DIM >::face_local_coordinate_of_flux_interpolation_point	(	const unsigned &	edge,
		const unsigned &	n,
		Vector< double > &	s
	)		const

pure virtual

Compute the face element coordinates of the nth flux interpolation point along an edge

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >.

◆ fill_in_contribution_to_residuals()

template<unsigned DIM>

void oomph::DarcyEquations< DIM >::fill_in_contribution_to_residuals ( Vector< double > & residuals )

inlinevirtual

Fill in contribution to residuals for the Darcy equations.

Reimplemented from oomph::GeneralisedElement.

     {
       this->fill_in_generic_residual_contribution(
         residuals, GeneralisedElement::Dummy_matrix, 0);
     }

References oomph::GeneralisedElement::Dummy_matrix, and oomph::DarcyEquations< DIM >::fill_in_generic_residual_contribution().

◆ fill_in_generic_residual_contribution()

template<unsigned DIM>

void oomph::DarcyEquations< DIM >::fill_in_generic_residual_contribution	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian,
		bool	flag
	)

protectedvirtual

Fill in residuals and, if flag==true, jacobian.

   {
     // Get the number of geometric nodes, total number of basis functions,
     // and number of edges basis functions
     const unsigned n_node = nnode();
     const unsigned n_q_basis = nq_basis();
     const unsigned n_q_basis_edge = nq_basis_edge();
     const unsigned n_p_basis = np_basis();
  
     // Storage for the geometric and computational bases and the test functions
     Shape psi(n_node), q_basis(n_q_basis, DIM), q_test(n_q_basis, DIM),
       p_basis(n_p_basis), p_test(n_p_basis), div_q_basis_ds(n_q_basis),
       div_q_test_ds(n_q_basis);
  
     // Get the number of integration points
     unsigned n_intpt = integral_pt()->nweight();
  
     // Storage for the local coordinates
     Vector<double> s(DIM);
  
     // Storage for the source function
     Vector<double> f(DIM);
  
     // Storage for the mass source function
     double mass_source_local;
  
     // Local equation and unknown numbers
     int local_eqn = 0; //, local_unknown = 0;
  
     // Loop over the integration points
     for (unsigned ipt = 0; ipt < n_intpt; ipt++)
     {
       // Find the local coordinates at the integration point
       for (unsigned i = 0; i < DIM; i++)
       {
         s[i] = integral_pt()->knot(ipt, i);
       }
  
       // Get the weight of the intetgration point
       double w = integral_pt()->weight(ipt);
  
       // Call the basis functions and test functions and get the
       // (geometric) jacobian of the current element
       double J = shape_basis_test_local_at_knot(ipt,
                                                 psi,
                                                 q_basis,
                                                 q_test,
                                                 p_basis,
                                                 p_test,
                                                 div_q_basis_ds,
                                                 div_q_test_ds);
  
       // Storage for interpolated values
       Vector<double> interpolated_x(DIM, 0.0);
       Vector<double> interpolated_q(DIM, 0.0);
       double interpolated_div_q_ds = 0.0;
       double interpolated_p = 0.0;
  
       // loop over the geometric basis functions to find interpolated x
       for (unsigned l = 0; l < n_node; l++)
       {
         for (unsigned i = 0; i < DIM; i++)
         {
           interpolated_x[i] += nodal_position(l, i) * psi[l];
         }
       }
  
       // loop over the nodes and use the vector basis functions to find the
       // interpolated flux
       for (unsigned i = 0; i < DIM; i++)
       {
         // Loop over the edge basis vectors
         for (unsigned l = 0; l < n_q_basis_edge; l++)
         {
           interpolated_q[i] += q_edge(l) * q_basis(l, i);
         }
         // Loop over the internal basis vectors
         for (unsigned l = n_q_basis_edge; l < n_q_basis; l++)
         {
           interpolated_q[i] += q_internal(l - n_q_basis_edge) * q_basis(l, i);
         }
       }
  
       // loop over the pressure basis and find the interpolated pressure
       for (unsigned l = 0; l < n_p_basis; l++)
       {
         interpolated_p += p_value(l) * p_basis(l);
       }
  
       // loop over the q edge divergence basis and the q internal divergence
       // basis to find interpolated div q
       for (unsigned l = 0; l < n_q_basis_edge; l++)
       {
         interpolated_div_q_ds += q_edge(l) * div_q_basis_ds(l);
       }
       for (unsigned l = n_q_basis_edge; l < n_q_basis; l++)
       {
         interpolated_div_q_ds +=
           q_internal(l - n_q_basis_edge) * div_q_basis_ds(l);
       }
  
       // Get the source function
       this->source(interpolated_x, f);
  
       // Get the mass source function
       this->mass_source(interpolated_x, mass_source_local);
  
       // Loop over the test functions
       for (unsigned l = 0; l < n_q_basis; l++)
       {
         if (l < n_q_basis_edge)
         {
           local_eqn = q_edge_local_eqn(l);
         }
         else // n_q_basis_edge <= l < n_basis
         {
           local_eqn = q_internal_local_eqn(l - n_q_basis_edge);
         }
  
         // If it's not a boundary condition
         if (local_eqn >= 0)
         {
           for (unsigned i = 0; i < DIM; i++)
           {
             residuals[local_eqn] +=
               (interpolated_q[i] - f[i]) * q_test(l, i) * w * J;
           }
  
           // deliberately no jacobian factor in this integral
           residuals[local_eqn] -= (interpolated_p * div_q_test_ds(l)) * w;
         }
       } // End of loop over test functions
  
       // loop over pressure test functions
       for (unsigned l = 0; l < n_p_basis; l++)
       {
         // get the local equation number
         local_eqn = p_local_eqn(l);
  
         // If it's not a boundary condition
         if (local_eqn >= 0)
         {
           // deliberately no jacobian factor in this integral
           residuals[local_eqn] += interpolated_div_q_ds * p_test(l) * w;
           residuals[local_eqn] -= mass_source_local * p_test(l) * w * J;
         }
       }
     } // End of loop over integration points
   }

References DIM, f(), i, J, s, and w.

Referenced by oomph::DarcyEquations< DIM >::fill_in_contribution_to_residuals().

◆ get_div_q_basis_local()

template<unsigned DIM>

virtual void oomph::DarcyEquations< DIM >::get_div_q_basis_local	(	const Vector< double > &	s,
		Shape &	div_q_basis_ds
	)		const

pure virtual

Returns the local form of the q basis and dbasis/ds at local coordinate s

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >, oomph::TRaviartThomasDarcyElement< ORDER >, and oomph::TRaviartThomasDarcyElement< ORDER >.

Referenced by oomph::DarcyEquations< DIM >::interpolated_div_q().

◆ get_p_basis()

template<unsigned DIM>

virtual void oomph::DarcyEquations< DIM >::get_p_basis	(	const Vector< double > &	s,
		Shape &	p_basis
	)		const

pure virtual

Return the pressure basis.

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >, oomph::TRaviartThomasDarcyElement< ORDER >, and oomph::TRaviartThomasDarcyElement< ORDER >.

Referenced by oomph::DarcyEquations< DIM >::interpolated_p().

◆ get_q_basis()

template<unsigned DIM>

void oomph::DarcyEquations< DIM >::get_q_basis	(	const Vector< double > &	s,
		Shape &	q_basis
	)		const

inline

Returns the transformed basis at local coordinate s.

     {
       const unsigned n_node = this->nnode();
       Shape psi(n_node, DIM);
       const unsigned n_q_basis = this->nq_basis();
       Shape q_basis_local(n_q_basis, DIM);
       this->get_q_basis_local(s, q_basis_local);
       (void)this->transform_basis(s, q_basis_local, psi, q_basis);
     }

References DIM, oomph::DarcyEquations< DIM >::get_q_basis_local(), oomph::FiniteElement::nnode(), oomph::DarcyEquations< DIM >::nq_basis(), and oomph::DarcyEquations< DIM >::transform_basis().

Referenced by oomph::DarcyEquations< DIM >::interpolated_q().

◆ get_q_basis_local()

template<unsigned DIM>

virtual void oomph::DarcyEquations< DIM >::get_q_basis_local	(	const Vector< double > &	s,
		Shape &	q_basis
	)		const

pure virtual

Returns the local form of the q basis at local coordinate s.

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >, oomph::TRaviartThomasDarcyElement< ORDER >, and oomph::TRaviartThomasDarcyElement< ORDER >.

Referenced by oomph::DarcyEquations< DIM >::get_q_basis().

◆ get_Z2_flux()

template<unsigned DIM>

void oomph::DarcyEquations< DIM >::get_Z2_flux	(	const Vector< double > &	s,
		Vector< double > &	flux
	)

inlinevirtual

Z2 flux (use actual flux)

Implements oomph::ElementWithZ2ErrorEstimator.

     {
       interpolated_q(s, flux);
     }

References ProblemParameters::flux(), oomph::DarcyEquations< DIM >::interpolated_q(), and s.

◆ interpolated_div_q() [1/2]

template<unsigned DIM>

double oomph::DarcyEquations< DIM >::interpolated_div_q ( const Vector< double > & s )

inline

Calculate the FE representation of div q and return it.

     {
       // Temporary storage for div q
       double div_q = 0;
  
       // Get the intepolated divergence
       interpolated_div_q(s, div_q);
  
       // Return it
       return div_q;
     }

References oomph::DarcyEquations< DIM >::interpolated_div_q(), and s.

◆ interpolated_div_q() [2/2]

template<unsigned DIM>

void oomph::DarcyEquations< DIM >::interpolated_div_q	(	const Vector< double > &	s,
		double &	div_q
	)		const

inline

Calculate the FE representation of div q.

     {
       // Zero the divergence
       div_q = 0;
  
       // Get the number of nodes, q basis function, and q edge basis functions
       unsigned n_node = nnode();
       const unsigned n_q_basis = nq_basis();
       const unsigned n_q_basis_edge = nq_basis_edge();
  
       // Storage for the divergence basis
       Shape div_q_basis_ds(n_q_basis);
  
       // Storage for the geometric basis and it's derivatives
       Shape psi(n_node);
       DShape dpsi(n_node, DIM);
  
       // Call the geometric shape functions and their derivatives
       this->dshape_local(s, psi, dpsi);
  
       // Storage for the inverse of the geometric jacobian (just so we can call
       // the local to eulerian mapping)
       DenseMatrix<double> inverse_jacobian(DIM);
  
       // Get the determinant of the geometric mapping
       double det = local_to_eulerian_mapping(dpsi, inverse_jacobian);
  
       // Get the divergence basis (wrt local coords) at local coords s
       get_div_q_basis_local(s, div_q_basis_ds);
  
       // Add the contribution to the divergence from the edge basis functions
       for (unsigned l = 0; l < n_q_basis_edge; l++)
       {
         div_q += 1.0 / det * div_q_basis_ds(l) * q_edge(l);
       }
  
       // Add the contribution to the divergence from the internal basis
       // functions
       for (unsigned l = n_q_basis_edge; l < n_q_basis; l++)
       {
         div_q += 1.0 / det * div_q_basis_ds(l) * q_internal(l - n_q_basis_edge);
       }
     }

References DIM, oomph::FiniteElement::dshape_local(), oomph::DarcyEquations< DIM >::get_div_q_basis_local(), oomph::FiniteElement::local_to_eulerian_mapping(), oomph::FiniteElement::nnode(), oomph::DarcyEquations< DIM >::nq_basis(), oomph::DarcyEquations< DIM >::nq_basis_edge(), oomph::DarcyEquations< DIM >::q_edge(), oomph::DarcyEquations< DIM >::q_internal(), and s.

Referenced by oomph::DarcyEquations< DIM >::interpolated_div_q().

◆ interpolated_p() [1/2]

template<unsigned DIM>

double oomph::DarcyEquations< DIM >::interpolated_p ( const Vector< double > & s ) const

inline

Calculate the FE representation of p and return it.

     {
       // Temporary storage for p
       double p = 0;
  
       // Get the interpolated pressure
       interpolated_p(s, p);
  
       // Return it
       return p;
     }

References oomph::DarcyEquations< DIM >::interpolated_p(), p, and s.

◆ interpolated_p() [2/2]

template<unsigned DIM>

void oomph::DarcyEquations< DIM >::interpolated_p	(	const Vector< double > &	s,
		double &	p
	)		const

inline

Calculate the FE representation of p.

     {
       // Get the number of p basis functions
       unsigned n_p_basis = np_basis();
  
       // Storage for the p basis
       Shape p_basis(n_p_basis);
  
       // Call the p basis
       get_p_basis(s, p_basis);
  
       // Zero the pressure
       p = 0;
  
       // Add the contribution to the pressure from each basis function
       for (unsigned l = 0; l < n_p_basis; l++)
       {
         p += p_value(l) * p_basis(l);
       }
     }

References oomph::DarcyEquations< DIM >::get_p_basis(), oomph::DarcyEquations< DIM >::np_basis(), p, oomph::DarcyEquations< DIM >::p_value(), and s.

Referenced by oomph::DarcyEquations< DIM >::interpolated_p().

◆ interpolated_q() [1/2]

template<unsigned DIM>

double oomph::DarcyEquations< DIM >::interpolated_q	(	const Vector< double > &	s,
		const unsigned	i
	)		const

inline

Calculate the FE representation of the i-th component of q.

     {
       unsigned n_q_basis = nq_basis();
       unsigned n_q_basis_edge = nq_basis_edge();
  
       Shape q_basis(n_q_basis, DIM);
  
       get_q_basis(s, q_basis);
       double q_i = 0.0;
       for (unsigned l = 0; l < n_q_basis_edge; l++)
       {
         q_i += q_edge(l) * q_basis(l, i);
       }
       for (unsigned l = n_q_basis_edge; l < n_q_basis; l++)
       {
         q_i += q_internal(l - n_q_basis_edge) * q_basis(l, i);
       }
  
       return q_i;
     }

References DIM, oomph::DarcyEquations< DIM >::get_q_basis(), i, oomph::DarcyEquations< DIM >::nq_basis(), oomph::DarcyEquations< DIM >::nq_basis_edge(), oomph::DarcyEquations< DIM >::q_edge(), oomph::DarcyEquations< DIM >::q_internal(), and s.

◆ interpolated_q() [2/2]

template<unsigned DIM>

void oomph::DarcyEquations< DIM >::interpolated_q	(	const Vector< double > &	s,
		Vector< double > &	q
	)		const

inline

Calculate the FE representation of q.

     {
       unsigned n_q_basis = nq_basis();
       unsigned n_q_basis_edge = nq_basis_edge();
  
       Shape q_basis(n_q_basis, DIM);
  
       get_q_basis(s, q_basis);
       for (unsigned i = 0; i < DIM; i++)
       {
         q[i] = 0.0;
         for (unsigned l = 0; l < n_q_basis_edge; l++)
         {
           q[i] += q_edge(l) * q_basis(l, i);
         }
         for (unsigned l = n_q_basis_edge; l < n_q_basis; l++)
         {
           q[i] += q_internal(l - n_q_basis_edge) * q_basis(l, i);
         }
       }
     }

References DIM, oomph::DarcyEquations< DIM >::get_q_basis(), i, oomph::DarcyEquations< DIM >::nq_basis(), oomph::DarcyEquations< DIM >::nq_basis_edge(), Eigen::numext::q, oomph::DarcyEquations< DIM >::q_edge(), oomph::DarcyEquations< DIM >::q_internal(), and s.

Referenced by oomph::DarcyEquations< DIM >::get_Z2_flux().

◆ mass_source()

template<unsigned DIM>

void oomph::DarcyEquations< DIM >::mass_source	(	const Vector< double > &	x,
		double &	b
	)		const

inline

Indirect access to the mass source function - returns 0 if no mass source function has been set

     {
       // If no function has been set, return zero vector
       if (Mass_source_fct_pt == 0)
       {
         b = 0.0;
       }
       else
       {
         // Get body force
         (*Mass_source_fct_pt)(x, b);
       }
     }

References b, oomph::DarcyEquations< DIM >::Mass_source_fct_pt, and plotDoE::x.

◆ mass_source_fct_pt() [1/2]

template<unsigned DIM>

MassSourceFctPt& oomph::DarcyEquations< DIM >::mass_source_fct_pt ( )

inline

Access function: Pointer to mass source function.

     {
       return Mass_source_fct_pt;
     }

References oomph::DarcyEquations< DIM >::Mass_source_fct_pt.

◆ mass_source_fct_pt() [2/2]

template<unsigned DIM>

MassSourceFctPt oomph::DarcyEquations< DIM >::mass_source_fct_pt ( ) const

inline

Access function: Pointer to mass source function (const version)

     {
       return Mass_source_fct_pt;
     }

References oomph::DarcyEquations< DIM >::Mass_source_fct_pt.

◆ nedge_flux_interpolation_point()

template<unsigned DIM>

virtual unsigned oomph::DarcyEquations< DIM >::nedge_flux_interpolation_point ( ) const

pure virtual

Returns the number of flux interpolation points along each edge of the element

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >, oomph::TRaviartThomasDarcyElement< ORDER >, and oomph::TRaviartThomasDarcyElement< ORDER >.

◆ np_basis()

template<unsigned DIM>

virtual unsigned oomph::DarcyEquations< DIM >::np_basis ( ) const

pure virtual

Return the total number of pressure basis functions.

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >, oomph::TRaviartThomasDarcyElement< ORDER >, and oomph::TRaviartThomasDarcyElement< ORDER >.

Referenced by oomph::DarcyEquations< DIM >::interpolated_p().

◆ nq_basis()

template<unsigned DIM>

unsigned oomph::DarcyEquations< DIM >::nq_basis ( ) const

inline

Return the total number of computational basis functions for q.

     {
       return nq_basis_edge() + nq_basis_internal();
     }

References oomph::DarcyEquations< DIM >::nq_basis_edge(), and oomph::DarcyEquations< DIM >::nq_basis_internal().

Referenced by oomph::DarcyEquations< DIM >::get_q_basis(), oomph::DarcyEquations< DIM >::interpolated_div_q(), and oomph::DarcyEquations< DIM >::interpolated_q().

◆ nq_basis_edge()

template<unsigned DIM>

virtual unsigned oomph::DarcyEquations< DIM >::nq_basis_edge ( ) const

pure virtual

Return the number of edge basis functions for q.

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >, oomph::TRaviartThomasDarcyElement< ORDER >, and oomph::TRaviartThomasDarcyElement< ORDER >.

Referenced by oomph::DarcyEquations< DIM >::interpolated_div_q(), oomph::DarcyEquations< DIM >::interpolated_q(), and oomph::DarcyEquations< DIM >::nq_basis().

◆ nq_basis_internal()

template<unsigned DIM>

virtual unsigned oomph::DarcyEquations< DIM >::nq_basis_internal ( ) const

pure virtual

Return the number of internal basis functions for q.

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >, oomph::TRaviartThomasDarcyElement< ORDER >, and oomph::TRaviartThomasDarcyElement< ORDER >.

Referenced by oomph::DarcyEquations< DIM >::nq_basis().

◆ num_Z2_flux_terms()

template<unsigned DIM>

unsigned oomph::DarcyEquations< DIM >::num_Z2_flux_terms ( )

inlinevirtual

Number off flux terms for Z2 error estimator (use actual flux)

Implements oomph::ElementWithZ2ErrorEstimator.

     {
       return DIM;
     }

References DIM.

◆ output() [1/2]

template<unsigned DIM>

void oomph::DarcyEquations< DIM >::output ( std::ostream & outfile )

inlinevirtual

Output with default number of plot points.

Reimplemented from oomph::FiniteElement.

     {
       unsigned nplot = 5;
       output(outfile, nplot);
     }

Referenced by oomph::TRaviartThomasDarcyElement< ORDER >::output().

◆ output() [2/2]

template<unsigned DIM>

void oomph::DarcyEquations< DIM >::output	(	std::ostream &	outfile,
		const unsigned &	nplot
	)

virtual

Output FE representation of soln: x,y,q1,q2,div_q,p at Nplot^DIM plot points

Reimplemented from oomph::FiniteElement.

   {
     // Vector of local coordinates
     Vector<double> s(DIM);
  
     // Tecplot header info
     outfile << tecplot_zone_string(nplot);
  
     // Loop over plot points
     unsigned num_plot_points = nplot_points(nplot);
  
     for (unsigned iplot = 0; iplot < num_plot_points; iplot++)
     {
       // Get local coordinates of plot point
       get_s_plot(iplot, nplot, s);
  
       // Output the components of the position
       for (unsigned i = 0; i < DIM; i++)
       {
         outfile << interpolated_x(s, i) << " ";
       }
  
       // Output the components of the FE representation of q at s
       for (unsigned i = 0; i < DIM; i++)
       {
         outfile << interpolated_q(s, i) << " ";
       }
  
       // Output FE representation of div q at s
       outfile << interpolated_div_q(s) << " ";
  
       // Output FE representation of p at s
       outfile << interpolated_p(s) << " ";
  
       outfile << std::endl;
     }
  
     // Write tecplot footer (e.g. FE connectivity lists)
     this->write_tecplot_zone_footer(outfile, nplot);
   }

References DIM, i, and s.

◆ output_fct()

template<unsigned DIM>

void oomph::DarcyEquations< DIM >::output_fct	(	std::ostream &	outfile,
		const unsigned &	nplot,
		FiniteElement::SteadyExactSolutionFctPt	exact_soln_pt
	)

virtual

Output FE representation of exact soln: x,y,q1,q2,div_q,p at Nplot^DIM plot points

Reimplemented from oomph::FiniteElement.

   {
     // Vector of local coordinates
     Vector<double> s(DIM);
  
     // Vector for coordintes
     Vector<double> x(DIM);
  
     // Tecplot header info
     outfile << this->tecplot_zone_string(nplot);
  
     // Exact solution Vector
     Vector<double> exact_soln(DIM + 2);
  
     // Loop over plot points
     unsigned num_plot_points = this->nplot_points(nplot);
  
     for (unsigned iplot = 0; iplot < num_plot_points; iplot++)
     {
       // Get local coordinates of plot point
       this->get_s_plot(iplot, nplot, s);
  
       // Get x position as Vector
       this->interpolated_x(s, x);
  
       // Get exact solution at this point
       (*exact_soln_pt)(x, exact_soln);
  
       // Output x,y,q_exact,p_exact,div_q_exact
       for (unsigned i = 0; i < DIM; i++)
       {
         outfile << x[i] << " ";
       }
       for (unsigned i = 0; i < DIM + 2; i++)
       {
         outfile << exact_soln[i] << " ";
       }
       outfile << std::endl;
     }
  
     // Write tecplot footer (e.g. FE connectivity lists)
     this->write_tecplot_zone_footer(outfile, nplot);
   }

References DIM, ProblemParameters::exact_soln(), i, s, and plotDoE::x.

◆ output_with_projected_flux()

template<unsigned DIM>

void oomph::DarcyEquations< DIM >::output_with_projected_flux	(	std::ostream &	outfile,
		const unsigned &	nplot,
		const Vector< double >	unit_normal
	)

Output FE representation of soln: x,y,q1,q2,div_q,p,q \cdot n.

Output incl. projection of fluxes into direction of the specified unit vector

   {
     // Vector of local coordinates
     Vector<double> s(DIM);
  
     // Tecplot header info
     outfile << this->tecplot_zone_string(nplot);
  
     // Loop over plot points
     unsigned num_plot_points = this->nplot_points(nplot);
  
     for (unsigned iplot = 0; iplot < num_plot_points; iplot++)
     {
       // Get local coordinates of plot point
       this->get_s_plot(iplot, nplot, s);
  
       // Output the components of the position
       for (unsigned i = 0; i < DIM; i++)
       {
         outfile << this->interpolated_x(s, i) << " ";
       }
  
       // Output the components of the FE representation of q at s
       for (unsigned i = 0; i < DIM; i++)
       {
         outfile << this->interpolated_q(s, i) << " ";
       }
  
       // Output FE representation of div q at s
       outfile << this->interpolated_div_q(s) << " ";
  
       // Output FE representation of p at s
       outfile << this->interpolated_p(s) << " ";
  
       // Fluxes projected into the direction of the face normal
       double flux = 0.0;
       for (unsigned i = 0; i < 2; i++)
       {
         flux += this->interpolated_q(s, i) * unit_normal[i];
       }
       outfile << flux << " ";
  
       outfile << std::endl;
     }
  
     // Write tecplot footer (e.g. FE connectivity lists)
     this->write_tecplot_zone_footer(outfile, nplot);
   }

References DIM, ProblemParameters::flux(), i, and s.

◆ p_data_pt()

template<unsigned DIM>

virtual Data* oomph::DarcyEquations< DIM >::p_data_pt ( ) const

pure virtual

Return pointer to the Data object that stores the pressure values.

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >.

◆ p_local_eqn()

template<unsigned DIM>

virtual int oomph::DarcyEquations< DIM >::p_local_eqn ( const unsigned & n ) const

pure virtual

Return the equation number of the n-th pressure degree of freedom.

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >, oomph::TRaviartThomasDarcyElement< ORDER >, and oomph::TRaviartThomasDarcyElement< ORDER >.

◆ p_value()

template<unsigned DIM>

virtual double oomph::DarcyEquations< DIM >::p_value ( const unsigned & n ) const

pure virtual

Return the nth pressure value.

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >, oomph::TRaviartThomasDarcyElement< ORDER >, and oomph::TRaviartThomasDarcyElement< ORDER >.

Referenced by oomph::DarcyEquations< DIM >::interpolated_p().

◆ pin_p_value()

template<unsigned DIM>

virtual void oomph::DarcyEquations< DIM >::pin_p_value ( const unsigned & n )

pure virtual

Pin the nth pressure value.

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >.

◆ pin_q_internal_value()

template<unsigned DIM>

virtual void oomph::DarcyEquations< DIM >::pin_q_internal_value ( const unsigned & n )

pure virtual

Pin the nth internal q value.

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >.

◆ pin_superfluous_darcy_dofs()

template<unsigned DIM>

virtual void oomph::DarcyEquations< DIM >::pin_superfluous_darcy_dofs ( )

inlinevirtual

Helper function to pin superfluous dofs (empty; can be overloaded in projectable elements where we introduce at least one dof per node to allow projection during unstructured refinement)

413 {}

◆ q_edge()

template<unsigned DIM>

virtual double oomph::DarcyEquations< DIM >::q_edge ( const unsigned & n ) const

pure virtual

Return the values of the n-th edge (flux) degree of freedom.

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >.

Referenced by oomph::DarcyEquations< DIM >::interpolated_div_q(), and oomph::DarcyEquations< DIM >::interpolated_q().

◆ q_edge_data_pt()

template<unsigned DIM>

virtual Vector<Data*> oomph::DarcyEquations< DIM >::q_edge_data_pt ( ) const

pure virtual

Return vector of pointers to the Data objects that store the edge flux values

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >.

◆ q_edge_index()

template<unsigned DIM>

virtual unsigned oomph::DarcyEquations< DIM >::q_edge_index ( const unsigned & n ) const

pure virtual

Return the nodal index at which the nth edge unknown is stored.

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >.

◆ q_edge_local_eqn()

template<unsigned DIM>

virtual int oomph::DarcyEquations< DIM >::q_edge_local_eqn ( const unsigned & n ) const

pure virtual

Return the equation number of the n-th edge (flux) degree of freedom.

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >.

◆ q_edge_node_number()

template<unsigned DIM>

virtual unsigned oomph::DarcyEquations< DIM >::q_edge_node_number ( const unsigned & n ) const

pure virtual

Return the number of the node where the nth edge unknown is stored.

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >.

◆ q_internal()

template<unsigned DIM>

virtual double oomph::DarcyEquations< DIM >::q_internal ( const unsigned & n ) const

pure virtual

Return the values of the internal degree of freedom.

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >.

Referenced by oomph::DarcyEquations< DIM >::interpolated_div_q(), and oomph::DarcyEquations< DIM >::interpolated_q().

◆ q_internal_data_pt()

template<unsigned DIM>

virtual Data* oomph::DarcyEquations< DIM >::q_internal_data_pt ( ) const

pure virtual

Return pointer to the Data object that stores the internal flux values.

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >.

◆ q_internal_index()

template<unsigned DIM>

virtual unsigned oomph::DarcyEquations< DIM >::q_internal_index ( ) const

pure virtual

Return the index of the internal data where the q_internal degrees of freedom are stored

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >.

◆ q_internal_local_eqn()

template<unsigned DIM>

virtual int oomph::DarcyEquations< DIM >::q_internal_local_eqn ( const unsigned & n ) const

pure virtual

Return the equation number of the n-th internal degree of freedom.

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >.

◆ required_nvalue()

template<unsigned DIM>

virtual unsigned oomph::DarcyEquations< DIM >::required_nvalue ( const unsigned & n ) const

pure virtual

Number of values required at node n.

Reimplemented from oomph::FiniteElement.

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >.

◆ scale_basis()

template<unsigned DIM>

virtual void oomph::DarcyEquations< DIM >::scale_basis ( Shape & basis ) const

pure virtual

Scale the edge basis to allow arbitrary edge mappings.

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >.

◆ self_test()

template<unsigned DIM>

unsigned oomph::DarcyEquations< DIM >::self_test ( )

inlinevirtual

Self test – empty for now.

Reimplemented from oomph::FiniteElement.

     {
       return 0;
     }

◆ set_p_value()

template<unsigned DIM>

virtual void oomph::DarcyEquations< DIM >::set_p_value	(	const unsigned &	n,
		const double &	value
	)

pure virtual

Set the nth pressure value.

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >.

◆ set_q_edge()

template<unsigned DIM>

virtual void oomph::DarcyEquations< DIM >::set_q_edge	(	const unsigned &	n,
		const double &	value
	)

pure virtual

Set the values of the edge (flux) degree of freedom.

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >.

◆ set_q_internal()

template<unsigned DIM>

virtual void oomph::DarcyEquations< DIM >::set_q_internal	(	const unsigned &	n,
		const double &	value
	)

pure virtual

Set the values of the internal degree of freedom.

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >.

◆ shape_basis_test_local()

template<unsigned DIM>

virtual double oomph::DarcyEquations< DIM >::shape_basis_test_local	(	const Vector< double > &	s,
		Shape &	psi,
		Shape &	q_basis,
		Shape &	q_test,
		Shape &	p_basis,
		Shape &	p_test,
		Shape &	div_q_basis_ds,
		Shape &	div_q_test_ds
	)		const

protectedpure virtual

Returns the geometric basis, and the q, p and divergence basis functions and test functions at local coordinate s

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >.

◆ shape_basis_test_local_at_knot()

template<unsigned DIM>

virtual double oomph::DarcyEquations< DIM >::shape_basis_test_local_at_knot	(	const unsigned &	ipt,
		Shape &	psi,
		Shape &	q_basis,
		Shape &	q_test,
		Shape &	p_basis,
		Shape &	p_test,
		Shape &	div_q_basis_ds,
		Shape &	div_q_test_ds
	)		const

protectedpure virtual

Returns the geometric basis, and the q, p and divergence basis functions and test functions at integration point ipt

Implemented in oomph::TRaviartThomasDarcyElement< ORDER >.

◆ source()

template<unsigned DIM>

void oomph::DarcyEquations< DIM >::source	(	const Vector< double > &	x,
		Vector< double > &	b
	)		const

inline

Indirect access to the source function - returns 0 if no source function has been set

     {
       // If no function has been set, return zero vector
       if (Source_fct_pt == 0)
       {
         // Get spatial dimension of element
         unsigned n = dim();
         for (unsigned i = 0; i < n; i++)
         {
           b[i] = 0.0;
         }
       }
       else
       {
         // Get body force
         (*Source_fct_pt)(x, b);
       }
     }

References b, oomph::FiniteElement::dim(), i, n, oomph::DarcyEquations< DIM >::Source_fct_pt, and plotDoE::x.

◆ source_fct_pt() [1/2]

template<unsigned DIM>

SourceFctPt& oomph::DarcyEquations< DIM >::source_fct_pt ( )

inline

Access function: Pointer to body force function.

     {
       return Source_fct_pt;
     }

References oomph::DarcyEquations< DIM >::Source_fct_pt.

◆ source_fct_pt() [2/2]

template<unsigned DIM>

SourceFctPt oomph::DarcyEquations< DIM >::source_fct_pt ( ) const

inline

Access function: Pointer to body force function (const version)

     {
       return Source_fct_pt;
     }

References oomph::DarcyEquations< DIM >::Source_fct_pt.

◆ transform_basis()

template<unsigned DIM>

double oomph::DarcyEquations< DIM >::transform_basis	(	const Vector< double > &	s,
		const Shape &	q_basis_local,
		Shape &	psi,
		Shape &	q_basis
	)		const

Performs a div-conserving transformation of the vector basis functions from the reference element to the actual element

   {
     // Get the number of nodes in the element
     const unsigned n_node = this->nnode();
  
     // Storage for derivatives of the (geometric) shape functions, and call
     // the shape functions
     DShape dpsi(n_node, DIM);
     this->dshape_local(s, psi, dpsi);
  
     // Storage for the (geometric) jacobian and its inverse
     DenseMatrix<double> jacobian(DIM), inverse_jacobian(DIM);
  
     // Get the jacobian of the geometric mapping and its determinant
     double det = local_to_eulerian_mapping(dpsi, jacobian, inverse_jacobian);
  
     // Get the number of computational basis vectors
     const unsigned n_q_basis = this->nq_basis();
  
     // Loop over the basis vectors
     for (unsigned l = 0; l < n_q_basis; l++)
     {
       // Loop over the spatial components
       for (unsigned i = 0; i < DIM; i++)
       {
         // Zero the basis
         q_basis(l, i) = 0.0;
       }
     }
  
     // Loop over the spatial components
     for (unsigned i = 0; i < DIM; i++)
     {
       // And again
       for (unsigned j = 0; j < DIM; j++)
       {
         // Get the element of the jacobian (must transpose it due to different
         // conventions) and divide by the determinant
         double jac_trans = jacobian(j, i) / det;
  
         // Loop over the computational basis vectors
         for (unsigned l = 0; l < n_q_basis; l++)
         {
           // Apply the appropriate div-conserving mapping
           q_basis(l, i) += jac_trans * q_basis_local(l, j);
         }
       }
     }
  
     // Scale the basis by the ratio of the length of the edge to the length of
     // the corresponding edge on the reference element
     scale_basis(q_basis);
  
     return det;
   }

References DIM, i, j, and s.

Referenced by oomph::DarcyEquations< DIM >::get_q_basis().

Member Data Documentation

◆ Mass_source_fct_pt

template<unsigned DIM>

MassSourceFctPt oomph::DarcyEquations< DIM >::Mass_source_fct_pt

private

Pointer to the mass source function.

Referenced by oomph::DarcyEquations< DIM >::mass_source(), and oomph::DarcyEquations< DIM >::mass_source_fct_pt().

◆ Source_fct_pt

template<unsigned DIM>

SourceFctPt oomph::DarcyEquations< DIM >::Source_fct_pt

private

Pointer to body force function.

Referenced by oomph::DarcyEquations< DIM >::source(), and oomph::DarcyEquations< DIM >::source_fct_pt().

The documentation for this class was generated from the following files:

Public Types

Public Member Functions

Protected Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

template<unsigned DIM> class oomph::DarcyEquations< DIM >

Member Typedef Documentation

◆ MassSourceFctPt

◆ SourceFctPt

Constructor & Destructor Documentation

◆ DarcyEquations()

Member Function Documentation

◆ compute_error()

◆ edge_flux_interpolation_point()

◆ edge_flux_interpolation_point_global() [1/2]

◆ edge_flux_interpolation_point_global() [2/2]

◆ face_index_of_edge()

◆ face_index_of_q_edge_basis_fct()

◆ face_local_coordinate_of_flux_interpolation_point()

◆ fill_in_contribution_to_residuals()

◆ fill_in_generic_residual_contribution()

◆ get_div_q_basis_local()

◆ get_p_basis()

◆ get_q_basis()

◆ get_q_basis_local()

◆ get_Z2_flux()

◆ interpolated_div_q() [1/2]

◆ interpolated_div_q() [2/2]

◆ interpolated_p() [1/2]

◆ interpolated_p() [2/2]

◆ interpolated_q() [1/2]

◆ interpolated_q() [2/2]

◆ mass_source()

◆ mass_source_fct_pt() [1/2]

◆ mass_source_fct_pt() [2/2]

◆ nedge_flux_interpolation_point()

◆ np_basis()

◆ nq_basis()

◆ nq_basis_edge()

◆ nq_basis_internal()

◆ num_Z2_flux_terms()

◆ output() [1/2]

◆ output() [2/2]

◆ output_fct()

◆ output_with_projected_flux()

◆ p_data_pt()

◆ p_local_eqn()

◆ p_value()

◆ pin_p_value()

◆ pin_q_internal_value()

◆ pin_superfluous_darcy_dofs()

◆ q_edge()

◆ q_edge_data_pt()

◆ q_edge_index()

◆ q_edge_local_eqn()

◆ q_edge_node_number()

◆ q_internal()

◆ q_internal_data_pt()

◆ q_internal_index()

◆ q_internal_local_eqn()

◆ required_nvalue()

◆ scale_basis()

◆ self_test()

◆ set_p_value()

◆ set_q_edge()

◆ set_q_internal()

◆ shape_basis_test_local()

◆ shape_basis_test_local_at_knot()

◆ source()

◆ source_fct_pt() [1/2]

◆ source_fct_pt() [2/2]

◆ transform_basis()

Member Data Documentation

◆ Mass_source_fct_pt

◆ Source_fct_pt

template<unsigned DIM>
class oomph::DarcyEquations< DIM >