#include <multi_domain_linearised_navier_stokes_elements.h>

Inheritance diagram for RefineableLinearisedQCrouzeixRaviartMultiDomainElement:

Public Member Functions
	RefineableLinearisedQCrouzeixRaviartMultiDomainElement ()
	Constructor: call the underlying constructors. More...

virtual void	get_base_flow_u (const double &time, const unsigned &ipt, const Vector< double > &x, Vector< double > &result) const

virtual void	get_base_flow_dudx (const double &time, const unsigned &ipt, const Vector< double > &x, DenseMatrix< double > &result) const

void	fill_in_contribution_to_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)
	Compute the element's residual vector and the Jacobian matrix. More...

Public Member Functions inherited from oomph::RefineableLinearisedQCrouzeixRaviartElement
	RefineableLinearisedQCrouzeixRaviartElement ()
	Constructor. More...

unsigned	ncont_interpolated_values () const
	Number of continuously interpolated values: 4*DIM (velocities) More...

void	rebuild_from_sons (Mesh *&mesh_pt)
	Rebuild from sons: Reconstruct pressure from the (merged) sons. More...

unsigned	nrecovery_order ()

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

Node *	vertex_node_pt (const unsigned &j) const
	Pointer to the j-th vertex node in the element. More...

void	get_interpolated_values (const Vector< double > &s, Vector< double > &values)

void	get_interpolated_values (const unsigned &t, const Vector< double > &s, Vector< double > &values)

void	further_setup_hanging_nodes ()

void	further_build ()

Public Member Functions inherited from oomph::LinearisedQCrouzeixRaviartElement
	LinearisedQCrouzeixRaviartElement ()

virtual unsigned	required_nvalue (const unsigned &n) const
	Return number of values (pinned or dofs) required at local node n. More...

double	p_linearised_nst (const unsigned &i_internal, const unsigned &i) const

void	pin_pressure_normalisation_dofs ()
	Pin the normalisation dofs. More...

void	pin_real_or_imag (const unsigned &real_index)

void	unpin_real_or_imag (const unsigned &real_index)

void	copy_efunction_to_normalisation ()

unsigned	npres_linearised_nst () const

void	fix_pressure (const unsigned &p_dof, const double &pvalue)

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

void	output (std::ostream &outfile)
	Redirect output to NavierStokesEquations output. More...

void	output (std::ostream &outfile, const unsigned &n_plot)
	Redirect output to NavierStokesEquations output. More...

void	output (FILE *file_pt)
	Redirect output to NavierStokesEquations output. More...

void	output (FILE *file_pt, const unsigned &n_plot)
	Redirect output to NavierStokesEquations output. More...

unsigned	ndof_types () const

Public Member Functions inherited from oomph::LinearisedNavierStokesEquations
	LinearisedNavierStokesEquations ()

const double &	re () const
	Reynolds number. More...

const double &	re_st () const
	Product of Reynolds and Strouhal number (=Womersley number) More...

const double &	lambda () const

const double &	omega () const

double *&	re_pt ()
	Pointer to Reynolds number. More...

double *&	re_st_pt ()
	Pointer to product of Reynolds and Strouhal number (=Womersley number) More...

double *&	lambda_pt ()
	Pointer to lambda. More...

double *&	omega_pt ()
	Pointer to frequency. More...

LinearisedNavierStokesEigenfunctionNormalisationElement *	normalisation_element_pt ()
	Pointer to normalisation element. More...

void	set_eigenfunction_normalisation_element (LinearisedNavierStokesEigenfunctionNormalisationElement *const &normalisation_el_pt)
	the boolean flag check_nodal_data is set to false. More...

const double &	viscosity_ratio () const

double *&	viscosity_ratio_pt ()
	Pointer to the viscosity ratio. More...

const double &	density_ratio () const

double *&	density_ratio_pt ()
	Pointer to the density ratio. More...

virtual unsigned	u_index_linearised_nst (const unsigned &i) const

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

void	disable_ALE ()

void	enable_ALE ()

virtual int	p_index_linearised_nst (const unsigned &i) const
	Which nodal value represents the pressure? More...

void	strain_rate (const Vector< double > &s, DenseMatrix< double > &strain_rate, const unsigned &real) const

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

void	fill_in_contribution_to_residuals (Vector< double > &residuals)
	Compute the element's residual Vector. More...

double	interpolated_u_linearised_nst (const Vector< double > &s, const unsigned &i) const

double	interpolated_p_linearised_nst (const Vector< double > &s, const unsigned &i) const

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...

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)

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	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	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

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 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_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_fct (std::ostream &outfile, const unsigned &n_plot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
	Output an exact solution over the element. More...

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::SteadyExactSolutionFctPt exact_soln_pt, Vector< double > &error, Vector< 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	self_test ()

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...

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 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::RefineableLinearisedNavierStokesEquations
	RefineableLinearisedNavierStokesEquations ()
	Empty Constructor. More...

unsigned	num_Z2_flux_terms ()
	Number of 'flux' terms for Z2 error estimation. More...

void	get_Z2_flux (const Vector< double > &s, Vector< double > &flux)

Public Member Functions inherited from oomph::RefineableElement
	RefineableElement ()

virtual	~RefineableElement ()
	Destructor, delete the allocated storage for the hanging equations. More...

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

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

Tree *	tree_pt ()
	Access function: Pointer to quadtree representation of this element. More...

void	set_tree_pt (Tree *my_tree_pt)
	Set pointer to quadtree representation of this element. More...

bool	refinement_is_enabled ()
	Flag to indicate suppression of any refinement. More...

void	disable_refinement ()
	Suppress of any refinement for this element. More...

void	enable_refinement ()
	Emnable refinement for this element. More...

template<class ELEMENT >
void	split (Vector< ELEMENT * > &son_pt) const

int	local_hang_eqn (Node *const &node_pt, const unsigned &i)

void	set_refinement_level (const int &refine_level)
	Set the refinement level. More...

unsigned	refinement_level () const
	Return the Refinement level. More...

void	select_for_refinement ()
	Select the element for refinement. More...

void	deselect_for_refinement ()
	Deselect the element for refinement. More...

void	select_sons_for_unrefinement ()
	Unrefinement will be performed by merging the four sons of this element. More...

void	deselect_sons_for_unrefinement ()

bool	to_be_refined ()
	Has the element been selected for refinement? More...

bool	sons_to_be_unrefined ()
	Has the element been selected for unrefinement? More...

virtual void	unbuild ()

virtual void	deactivate_element ()

virtual bool	nodes_built ()
	Return true if all the nodes have been built, false if not. More...

long	number () const
	Element number (for debugging/plotting) More...

void	set_number (const long &mynumber)
	Set element number (for debugging/plotting) More...

virtual Node *	interpolating_node_pt (const unsigned &n, const int &value_id)

virtual double	local_one_d_fraction_of_interpolating_node (const unsigned &n1d, const unsigned &i, const int &value_id)

virtual Node *	get_interpolating_node_at_local_coordinate (const Vector< double > &s, const int &value_id)

virtual unsigned	ninterpolating_node (const int &value_id)

virtual unsigned	ninterpolating_node_1d (const int &value_id)

virtual void	interpolating_basis (const Vector< double > &s, Shape &psi, const int &value_id) const

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

void	assign_nodal_local_eqn_numbers (const bool &store_local_dof_pt)

virtual RefineableElement *	root_element_pt ()

virtual RefineableElement *	father_element_pt () const
	Return a pointer to the father element. More...

void	get_father_at_refinement_level (unsigned &refinement_level, RefineableElement *&father_at_reflevel_pt)

virtual void	initial_setup (Tree *const &adopted_father_pt=0, const unsigned &initial_p_order=0)

virtual void	pre_build (Mesh &mesh_pt, Vector< Node > &new_node_pt)
	Pre-build the element. More...

void	get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates)

unsigned	nshape_controlling_nodes ()

std::map< Node *, unsigned >	shape_controlling_node_lookup ()

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 double	geometric_jacobian (const Vector< double > &x)

Public Member Functions inherited from oomph::RefineableQElement< 2 >
	RefineableQElement ()
	Constructor: Pass refinement level (default 0 = root) More...

	RefineableQElement (const RefineableQElement< 2 > &dummy)=delete
	Broken copy constructor. More...

virtual	~RefineableQElement ()
	Broken assignment operator. More...

unsigned	required_nsons () const
	A refineable quad element has four sons. More...

virtual Node *	node_created_by_neighbour (const Vector< double > &s_fraction, bool &is_periodic)

virtual Node *	node_created_by_son_of_neighbour (const Vector< double > &s_fraction, bool &is_periodic)

virtual void	build (Mesh &mesh_pt, Vector< Node > &new_node_pt, bool &was_already_built, std::ofstream &new_nodes_file)

void	check_integrity (double &max_error)

void	output_corners (std::ostream &outfile, const std::string &colour) const
	Print corner nodes, use colour. More...

QuadTree *	quadtree_pt ()
	Pointer to quadtree representation of this element. More...

QuadTree *	quadtree_pt () const
	Pointer to quadtree representation of this element. More...

void	setup_hanging_nodes (Vector< std::ofstream * > &output_stream)

void	get_boundaries (const int &edge, std::set< unsigned > &boundaries) const

void	get_bcs (int bound, Vector< int > &bound_cons) const

void	interpolated_zeta_on_edge (const unsigned &boundary, const int &edge, const Vector< double > &s, Vector< double > &zeta)

Public Member Functions inherited from oomph::QuadElementBase
	QuadElementBase ()
	Constructor. Empty. More...

Public Member Functions inherited from oomph::QElementBase
	QElementBase ()
	Constructor: Initialise pointers to macro element reference coords. More...

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

virtual	~QElementBase ()
	Broken assignment operator. More...

bool	local_coord_is_valid (const Vector< double > &s)
	Check whether the local coordinate are valid or not. More...

void	move_local_coord_back_into_element (Vector< double > &s) const

virtual void	set_macro_elem_pt (MacroElement *macro_elem_pt)

double &	s_macro_ll (const unsigned &i)

double &	s_macro_ur (const unsigned &i)

double	s_macro_ll (const unsigned &i) const

double	s_macro_ur (const unsigned &i) const

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

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

unsigned	nnode_on_face () const

ElementGeometry::ElementGeometry	element_geometry () const
	It's a Q element! More...

Public Member Functions inherited from oomph::QElementGeometricBase
	QElementGeometricBase ()
	Empty default constructor. More...

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

Public Member Functions inherited from oomph::ElementWithExternalElement
	ElementWithExternalElement ()

virtual	~ElementWithExternalElement ()
	The destructor, clean up any allocated memory. More...

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

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

bool	storage_has_been_allocated () const
	Helper function to check if storage has actually been allocated. More...

FiniteElement *&	external_element_pt (const unsigned &interaction_index, const unsigned &ipt)

FiniteElement *const &	external_element_pt (const unsigned &interaction_index, const unsigned &ipt) const
	Access function to source element, const version. More...

Vector< double > &	external_element_local_coord (const unsigned &interaction_index, const unsigned &ipt)

Vector< double > const &	external_element_local_coord (const unsigned &interaction_index, const unsigned &ipt) const
	Access function to get source element's coords, const version. More...

void	output_external_elements (std::ostream &outfile, const unsigned &interaction_index)

void	initialise_external_element_storage ()

void	flush_all_external_element_storage ()
	Flush the storage for external elements. More...

void	set_ninteraction (const unsigned &n_interaction)

unsigned	ninteraction () const
	Return the number of interactions in the element. More...

virtual void	identify_all_field_data_for_external_interaction (Vector< std::set< FiniteElement * >> const &external_elements_pt, std::set< std::pair< Data *, unsigned >> &paired_interaction_data)

virtual void	identify_all_geometric_data_for_external_interaction (Vector< std::set< FiniteElement * >> const &external_elements_pt, std::set< Data * > &external_geometric_data_pt)

unsigned	nexternal_interaction_field_data () const

Vector< Data * >	external_interaction_field_data_pt () const

unsigned	nexternal_interaction_geometric_data () const

bool	add_external_geometric_data ()
	Are we including external geometric data in the element's Jacobian. More...

bool	add_external_interaction_data ()
	Are we including external data in the element's Jacobian. More...

Vector< Data * >	external_interaction_geometric_data_pt () const

void	ignore_external_geometric_data ()

void	ignore_external_interaction_data ()

void	include_external_geometric_data ()

void	include_external_interaction_data ()

bool	external_geometric_data_is_included () const

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

Additional Inherited Members
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 Types inherited from oomph::RefineableQElement< 2 >
typedef void(RefineableQElement< 2 >::*	VoidMemberFctPt) ()

Static Public Member Functions inherited from oomph::RefineableLinearisedNavierStokesEquations
static void	pin_redundant_nodal_pressures (const Vector< GeneralisedElement * > &element_pt)

static void	unpin_all_pressure_dofs (const Vector< GeneralisedElement * > &element_pt)
	Unpin all pressure dofs in elements listed in Vector. More...

Static Public Member Functions inherited from oomph::RefineableElement
static double &	max_integrity_tolerance ()
	Max. allowed discrepancy in element integrity check. More...

Public Attributes inherited from oomph::LinearisedNavierStokesEquations
void(*&)(const double &time, const Vector< double > &x, Vector< double > &f)	base_flow_u_fct_pt ()
	Access function for the base flow solution pointer. More...

void(*&)(const double &time, const Vector< double > &x, DenseMatrix< double > &f)	base_flow_dudx_fct_pt ()

Static Public Attributes inherited from oomph::LinearisedNavierStokesEquations
static Vector< double >	Gamma
	Vector to decide whether the stress-divergence form is used or not. More...

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 Member Functions inherited from oomph::LinearisedQCrouzeixRaviartElement
double	dshape_and_dtest_eulerian_linearised_nst (const Vector< double > &s, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const

double	dshape_and_dtest_eulerian_at_knot_linearised_nst (const unsigned &ipt, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const

void	pshape_linearised_nst (const Vector< double > &s, Shape &psi) const
	Compute the pressure shape functions at local coordinate s. More...

void	pshape_linearised_nst (const Vector< double > &s, Shape &psi, Shape &test) const
	Compute the pressure shape and test functions at local coordinate s. More...

Protected Member Functions inherited from oomph::LinearisedNavierStokesEquations
int	eigenvalue_local_eqn (const unsigned &i)

Protected Member Functions inherited from oomph::FiniteElement
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 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

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)

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_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)

Protected Member Functions inherited from oomph::RefineableLinearisedNavierStokesEquations
virtual Node *	pressure_node_pt (const unsigned &n_p)

virtual void	pin_elemental_redundant_nodal_pressure_dofs ()

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

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

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

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

void	assign_hanging_local_eqn_numbers (const bool &store_local_dof_pt)
	Assign the local equation numbers for hanging node variables. More...

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

Protected Member Functions inherited from oomph::RefineableQElement< 2 >
void	setup_father_bounds ()

void	get_edge_bcs (const int &edge, Vector< int > &bound_cons) const
	Determine Vector of boundary conditions along edge (N/S/W/E) More...

void	setup_hang_for_value (const int &value_id)

virtual void	quad_hang_helper (const int &value_id, const int &my_edge, std::ofstream &output_hangfile)

Protected Member Functions inherited from oomph::ElementWithExternalElement
void	assign_internal_and_external_local_eqn_numbers (const bool &store_local_dof_pt)

void	assign_external_interaction_data_local_eqn_numbers (const bool &store_local_dof_pt)

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

void	fill_in_jacobian_from_external_interaction_by_fd (DenseMatrix< double > &jacobian)

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

void	fill_in_jacobian_from_external_interaction_field_by_fd (DenseMatrix< double > &jacobian)

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

void	fill_in_jacobian_from_external_interaction_geometric_by_fd (DenseMatrix< double > &jacobian)

virtual void	update_before_external_interaction_field_fd ()

virtual void	reset_after_external_interaction_field_fd ()

virtual void	update_in_external_interaction_field_fd (const unsigned &i)

virtual void	reset_in_external_interaction_field_fd (const unsigned &i)

virtual void	update_before_external_interaction_geometric_fd ()

virtual void	reset_after_external_interaction_geometric_fd ()

virtual void	update_in_external_interaction_geometric_fd (const unsigned &i)

virtual void	reset_in_external_interaction_geometric_fd (const unsigned &i)

Static Protected Member Functions inherited from oomph::RefineableElement
static void	check_value_id (const int &n_continuously_interpolated_values, const int &value_id)

Protected Attributes inherited from oomph::LinearisedQCrouzeixRaviartElement
Vector< unsigned >	P_linearised_nst_internal_index

Protected Attributes inherited from oomph::LinearisedNavierStokesEquations
double *	Viscosity_Ratio_pt

double *	Density_Ratio_pt

double *	Re_pt
	Pointer to global Reynolds number. More...

double *	ReSt_pt
	Pointer to global Reynolds number x Strouhal number (=Womersley) More...

double *	Lambda_pt
	Pointer to eigenvalue. More...

double *	Omega_pt
	Pointer to frequency. More...

LinearisedNavierStokesEigenfunctionNormalisationElement *	Normalisation_element_pt
	Pointer to the normalisation element. More...

unsigned	Data_number_of_eigenvalue
	Index of datum where eigenvalue is stored. More...

unsigned	Index_of_eigenvalue

void(*	Base_flow_u_fct_pt )(const double &time, const Vector< double > &x, Vector< double > &result)
	Pointer to base flow solution (velocity components) function. More...

void(*	Base_flow_dudx_fct_pt )(const double &time, const Vector< double > &x, DenseMatrix< double > &result)

bool	ALE_is_disabled

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

Protected Attributes inherited from oomph::RefineableElement
Tree *	Tree_pt
	A pointer to a general tree object. More...

unsigned	Refine_level
	Refinement level. More...

bool	To_be_refined
	Flag for refinement. More...

bool	Refinement_is_enabled
	Flag to indicate suppression of any refinement. More...

bool	Sons_to_be_unrefined
	Flag for unrefinement. More...

long	Number
	Global element number – for plotting/validation purposes. More...

Protected Attributes inherited from oomph::ElementWithExternalElement
bool	Add_external_interaction_data
	Boolean flag to indicate whether to include the external data. More...

bool	Add_external_geometric_data
	Boolean flag to indicate whether to include the external geometric data. More...

Data **	External_interaction_field_data_pt

Data **	External_interaction_geometric_data_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

Static Protected Attributes inherited from oomph::RefineableElement
static double	Max_integrity_tolerance = 1.0e-8
	Max. allowed discrepancy in element integrity check. More...

Static Protected Attributes inherited from oomph::RefineableQElement< 2 >
static std::map< unsigned, DenseMatrix< int > >	Father_bound

Detailed Description

////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////// Build a RefineableLinearisedQCrouzeixRaviart element that inherits from ElementWithExternalElement so that it can "communicate" with an axisymmetric Navier-Stokes element that provides the base flow velocities and their derivatives w.r.t. global coordinates (r and z)

Constructor & Destructor Documentation

◆ RefineableLinearisedQCrouzeixRaviartMultiDomainElement()

RefineableLinearisedQCrouzeixRaviartMultiDomainElement::RefineableLinearisedQCrouzeixRaviartMultiDomainElement ( )

inline

Constructor: call the underlying constructors.

Do not include any external geometric data when computing the element's Jacobian.

     : RefineableLinearisedQCrouzeixRaviartElement(),
       ElementWithExternalElement()
   {
     // There are two interactions: the base flow velocities and their
     // derivatives w.r.t. global coordinates
     this->set_ninteraction(2);
  
     // Do not include any external interaction data when computing
     // the element's Jacobian
     // ElementWithExternalElement::ignore_external_interaction_data();
  
     ElementWithExternalElement::ignore_external_geometric_data();
   }

References oomph::ElementWithExternalElement::ignore_external_geometric_data().

Member Function Documentation

◆ fill_in_contribution_to_jacobian()

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

inlinevirtual

Compute the element's residual vector and the Jacobian matrix.

Reimplemented from oomph::ElementWithExternalElement.

   {
     // Get the analytical contribution from the basic patricklinearised element
     RefineableLinearisedQCrouzeixRaviartElement::
       fill_in_contribution_to_jacobian(residuals, jacobian);
  
     // Get the off-diagonal terms by finite differencing
     this->fill_in_jacobian_from_external_interaction_by_fd(residuals, jacobian);
   }

References oomph::FiniteElement::fill_in_contribution_to_jacobian().

◆ get_base_flow_dudx()

virtual void RefineableLinearisedQCrouzeixRaviartMultiDomainElement::get_base_flow_dudx	(	const double &	time,
		const unsigned &	ipt,
		const Vector< double > &	x,
		DenseMatrix< double > &	result
	)		const

inlinevirtual

Overload get_base_flow_dudx(...) to return the derivatives of the external element's velocity components w.r.t. global coordinates at the integration point

Reimplemented from oomph::LinearisedNavierStokesEquations.

   {
     // Set interaction index to 1
     const unsigned interaction = 1;
  
     // Get a pointer to the external element that computes the base flow.
     // We know that it's an axisymmetric Navier-Stokes element.
     const QCrouzeixRaviartElement<DIM>* base_flow_el_pt =
       dynamic_cast<QCrouzeixRaviartElement<DIM>*>(
         external_element_pt(interaction, ipt));
  
     // Provide storage for local coordinates in the external element
     // which correspond to the integration point ipt
     Vector<double> s_external(2);
  
     // Determine local coordinates in the external element which correspond
     // to the integration point ipt
     s_external = external_element_local_coord(interaction, ipt);
  
     // Loop over velocity components
     for (unsigned i = 0; i < DIM; i++)
     {
       // Loop over coordinate directions and get derivatives of velocity
       // components from the external element
       for (unsigned j = 0; j < DIM; j++)
       {
         result(i, j) = base_flow_el_pt->interpolated_dudx_nst(s_external, i, j);
       }
     }
  
   } // End of overloaded get_base_flow_dudx function

References DIM, i, oomph::NavierStokesEquations< DIM >::interpolated_dudx_nst(), and j.

◆ get_base_flow_u()

virtual void RefineableLinearisedQCrouzeixRaviartMultiDomainElement::get_base_flow_u	(	const double &	time,
		const unsigned &	ipt,
		const Vector< double > &	x,
		Vector< double > &	result
	)		const

inlinevirtual

Overload get_base_flow_u(...) to return the external element's velocity components at the integration point

Reimplemented from oomph::LinearisedNavierStokesEquations.

   {
     // Set interaction index to 0
     const unsigned interaction = 0;
  
     // Get a pointer to the external element that computes the base flow.
     // We know that it's an axisymmetric Navier-Stokes element.
     const QCrouzeixRaviartElement<DIM>* base_flow_el_pt =
       dynamic_cast<QCrouzeixRaviartElement<DIM>*>(
         external_element_pt(interaction, ipt));
  
     // Provide storage for local coordinates in the external element
     // which correspond to the integration point ipt
     Vector<double> s_external(2);
  
     // Determine local coordinates in the external element which correspond
     // to the integration point ipt
     s_external = external_element_local_coord(interaction, ipt);
  
     // Get the three velocity components interpolated from the external element
     for (unsigned i = 0; i < DIM; i++)
     {
       result[i] = base_flow_el_pt->interpolated_u_nst(s_external, i);
     }
  
   } // End of overloaded get_base_flow_u function

References DIM, i, and oomph::NavierStokesEquations< DIM >::interpolated_u_nst().

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

multi_domain_linearised_navier_stokes_elements.h

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ RefineableLinearisedQCrouzeixRaviartMultiDomainElement()

Member Function Documentation

◆ fill_in_contribution_to_jacobian()

◆ get_base_flow_dudx()

◆ get_base_flow_u()