Refineable version of Unsteady Heat equations. More...

#include <refineable_discontinuous_galerkin_space_time_unsteady_heat_mixed_order_elements.h>

Inheritance diagram for oomph::RefineableSpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >:

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

	RefineableSpaceTimeUnsteadyHeatMixedOrderEquations (const RefineableSpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM > &dummy)=delete
	Broken copy 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)

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_build ()
	Further build: Copy source function pointer from father element. More...

Public Member Functions inherited from oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >
	SpaceTimeUnsteadyHeatMixedOrderEquations ()

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

void	disable_ALE ()

void	enable_ALE ()

void	compute_norm (double &norm)
	Compute norm of FE solution. More...

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

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

void	output (FILE *file_pt)
	C_style output with default number of plot points. More...

void	output (FILE *file_pt, const unsigned &nplot)

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

virtual void	output_fct (std::ostream &outfile, const unsigned &nplot, const double &time, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt)

void	compute_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)
	Get error and norm against exact solution. More...

void	compute_error (std::ostream &outfile, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, double &norm)
	Get error and norm against exact solution. More...

void	output_element_paraview (std::ofstream &outfile, const unsigned &nplot)

unsigned	nscalar_paraview () const

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

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

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

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

SpaceTimeUnsteadyHeatSourceFctPt &	source_fct_pt ()
	Access function: Pointer to source function. More...

SpaceTimeUnsteadyHeatSourceFctPt	source_fct_pt () const
	Access function: Pointer to source function. Const version. More...

virtual void	get_source_ust_heat (const double &t, const unsigned &ipt, const Vector< double > &x, double &source) const

const double &	alpha () const
	Alpha parameter (thermal inertia) More...

double *&	alpha_pt ()
	Pointer to Alpha parameter (thermal inertia) More...

const double &	beta () const
	Beta parameter (thermal conductivity) More...

double *&	beta_pt ()
	Pointer to Beta parameter (thermal conductivity) More...

void	get_flux (const Vector< double > &s, Vector< double > &flux) const
	Get flux: flux[i]=du/dx_i. More...

void	fill_in_contribution_to_residuals (Vector< double > &residuals)
	Compute element residual Vector (wrapper) More...

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

double	interpolated_u_ust_heat (const Vector< double > &s) const
	Return FE representation of function value u(s) at local coordinate s. More...

virtual unsigned	u_index_ust_heat () const

double	interpolated_u_ust_heat (const unsigned &t, const Vector< double > &s) const

double	du_dt_ust_heat (const unsigned &n) const

double	interpolated_du_dt_ust_heat (const Vector< double > &s) const

unsigned	self_test ()
	Self-test: Return 0 for OK. More...

virtual double	dshape_and_dtest_eulerian_ust_heat (const Vector< double > &s, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const =0

virtual double	dshape_and_dtest_eulerian_at_knot_ust_heat (const unsigned &ipt, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const =0

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	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 unsigned	required_nvalue (const unsigned &n) 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 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_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 void	output (const unsigned &t, std::ostream &outfile, const unsigned &n_plot) const

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, 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	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 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::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...

virtual unsigned	required_nsons () const

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)

virtual void	build (Mesh &mesh_pt, Vector< Node > &new_node_pt, bool &was_already_built, std::ofstream &new_nodes_file)=0

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	rebuild_from_sons (Mesh *&mesh_pt)=0

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 unsigned	ncont_interpolated_values () const =0

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

virtual void	check_integrity (double &max_error)=0

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...

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

virtual void	further_setup_hanging_nodes ()

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 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)

Private Member Functions
virtual void	fill_in_generic_residual_contribution_ust_heat (Vector< double > &residuals, DenseMatrix< double > &jacobian, const unsigned &flag)

Additional Inherited Members
Public Types inherited from oomph::SpaceTimeUnsteadyHeatEquationsBase
typedef void(*	SpaceTimeUnsteadyHeatSourceFctPt) (const double &time, const Vector< double > &x, double &u)

typedef void(*	SpaceTimeUnsteadyHeatSourceFctPt) (const double &time, const Vector< double > &x, double &u)

typedef void(*	SpaceTimeUnsteadyHeatSourceFctPt) (const double &time, const Vector< double > &x, double &u)

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

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

Static Public Member Functions inherited from oomph::RefineableElement
static double &	max_integrity_tolerance ()
	Max. allowed discrepancy in element integrity check. 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::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >
virtual void	shape_ust_heat (const Vector< double > &s, Shape &psi) const =0
	Shape functions w.r.t. to local coords. More...

virtual void	dshape_local_ust_heat (const Vector< double > &s, Shape &psi, DShape &dpsidx) const =0
	Shape functions & derivs. w.r.t. to local coords. More...

virtual void	dtest_local_ust_heat (const Vector< double > &s, Shape &test, DShape &dtestdx) const =0
	Test functions & derivs. w.r.t. to local coords. More...

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_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)

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)

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::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >
SpaceTimeUnsteadyHeatSourceFctPt	Source_fct_pt
	Pointer to source function: More...

bool	ALE_is_disabled

double *	Alpha_pt
	Pointer to Alpha parameter (thermal inertia) More...

double *	Beta_pt
	Pointer to Beta parameter (thermal conductivity) More...

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...

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...

Detailed Description

template<unsigned SPATIAL_DIM>
class oomph::RefineableSpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >

Refineable version of Unsteady Heat equations.

Constructor & Destructor Documentation

◆ RefineableSpaceTimeUnsteadyHeatMixedOrderEquations() [1/2]

template<unsigned SPATIAL_DIM>

oomph::RefineableSpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::RefineableSpaceTimeUnsteadyHeatMixedOrderEquations ( )

inline

Constructor.

       : SpaceTimeUnsteadyHeatMixedOrderEquations<SPATIAL_DIM>(),
         RefineableElement(),
         ElementWithZ2ErrorEstimator()
     {
     }

◆ RefineableSpaceTimeUnsteadyHeatMixedOrderEquations() [2/2]

template<unsigned SPATIAL_DIM>

oomph::RefineableSpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::RefineableSpaceTimeUnsteadyHeatMixedOrderEquations ( const RefineableSpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM > & dummy )

delete

Broken copy constructor.

Member Function Documentation

◆ fill_in_generic_residual_contribution_ust_heat()

template<unsigned SPATIAL_DIM>

void oomph::RefineableSpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::fill_in_generic_residual_contribution_ust_heat	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian,
		const unsigned &	flag
	)

privatevirtual

Add element's contribution to elemental residual vector and/or Jacobian matrix flag=0: compute residual vector only flag=1: compute both

Add element's contribution to the elemental residual vector and/or Jacobian matrix. flag=0: compute residual vector only flag=1: compute both

Reimplemented from oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >.

   {
     // Find out how many nodes there are in the element
     unsigned n_node = nnode();
  
     // Find the index at which the unknown is stored
     unsigned u_nodal_index = this->u_index_ust_heat();
  
     // Set up memory for the shape functions
     Shape psi(n_node);
  
     // Set up memory for the test functions
     Shape test(n_node);
  
     // Allocate space for the derivatives of the shape functions
     DShape dpsidx(n_node, SPATIAL_DIM + 1);
  
     // Allocate space for the derivatives of the test functions
     DShape dtestdx(n_node, SPATIAL_DIM + 1);
  
     // Set the value of n_intpt
     unsigned n_intpt = integral_pt()->nweight();
  
     // Storage for the local coordinates
     Vector<double> s(SPATIAL_DIM + 1, 0.0);
  
     // Get the Alpha parameter
     double alpha_local = this->alpha();
  
     // Get the Beta parameter
     double beta_local = this->beta();
  
     // Integer to hold the local equation
     int local_eqn = 0;
  
     // Integer to hold the local unknowns
     int local_unknown = 0;
  
     // Local storage for pointer to hang info object
     HangInfo* hang_info_pt = 0;
  
     // Local storage for pointer to (another) hang info object
     HangInfo* hang_info2_pt = 0;
  
     // Loop over the integration points
     for (unsigned ipt = 0; ipt < n_intpt; ipt++)
     {
       // Assign values of s
       for (unsigned i = 0; i < SPATIAL_DIM + 1; i++)
       {
         // Calculate the i-th local coordinate
         s[i] = integral_pt()->knot(ipt, i);
       }
  
       // Get the integral weight
       double w = integral_pt()->weight(ipt);
  
       // Call the derivatives of the shape and test functions
       double J = this->dshape_and_dtest_eulerian_at_knot_ust_heat(
         ipt, psi, dpsidx, test, dtestdx);
  
       // Premultiply the weights and the Jacobian
       double W = w * J;
  
       // Storage for the interpolated time value
       double interpolated_t = 0.0;
  
       // Storage for the interpolated solution value
       double interpolated_u = 0.0;
  
       // Storage for the interpolated time-derivative of the solution
       double interpolated_dudt = 0.0;
  
       // Storage for the spatial coordinates
       Vector<double> interpolated_x(SPATIAL_DIM, 0.0);
  
       // Storage for the spatial derivatives of the solution
       Vector<double> interpolated_dudx(SPATIAL_DIM + 1, 0.0);
  
       // Storage for the mesh velocity
       Vector<double> mesh_velocity(SPATIAL_DIM, 0.0);
  
       //-------------------------------------------------
       // Calculate derivatives and source function value:
       //-------------------------------------------------
       // Loop over the nodes
       for (unsigned l = 0; l < n_node; l++)
       {
         // Get the nodal value at the l-th node
         double u_value = nodal_value(l, u_nodal_index);
  
         // Update the interpolated u value
         interpolated_u += u_value * psi(l);
  
         // Loop over the coordinate directions (both spatial AND time)
         for (unsigned j = 0; j < SPATIAL_DIM; j++)
         {
           // Update the interpolated x value
           interpolated_x[j] += nodal_position(l, j) * psi(l);
  
           // Update the interpolated du/dx_j value
           interpolated_dudx[j] += u_value * dpsidx(l, j);
         }
  
         // Update the interpolated time value
         interpolated_t += nodal_position(l, SPATIAL_DIM) * psi(l);
  
         // Update the interpolated du/dt value
         interpolated_dudt += u_value * dpsidx(l, SPATIAL_DIM);
       } // for (unsigned l=0;l<n_node;l++)
  
       // If ALE is enabled
       if (!(this->ALE_is_disabled))
       {
         // Loop over the coordinate directions
         for (unsigned j = 0; j < SPATIAL_DIM; j++)
         {
           // Loop over the nodes
           for (unsigned l = 0; l < n_node; l++)
           {
             // Update the mesh velocity
             mesh_velocity[j] += nodal_position(l, j) * dpsidx(l, SPATIAL_DIM);
           }
         } // for (unsigned j=0;j<SPATIAL_DIM;j++)
       } // if (!ALE_is_disabled)
  
       // Initialise the source term value
       double source = 0.0;
  
       // Get the interpolated source term value
       this->get_source_ust_heat(interpolated_t, ipt, interpolated_x, source);
  
       //--------------------------------
       // Assemble residuals and Jacobian
       //--------------------------------
       // Loop over the nodes (or equivalently the test functions)
       for (unsigned l = 0; l < n_node; l++)
       {
         // Storage for the number of master nodes
         unsigned n_master = 1;
  
         // Storage for the hang weight associated with the shape function
         double hang_weight = 1.0;
  
         // Check if the node is hanging
         bool is_node_hanging = this->node_pt(l)->is_hanging();
  
         // If the node is hanging, get the number of master nodes
         if (is_node_hanging)
         {
           // Get the hang info pointer associated with the l-th node in the
           // element
           hang_info_pt = this->node_pt(l)->hanging_pt();
  
           // Get the number of master nodes associated with the node
           n_master = hang_info_pt->nmaster();
         }
         // If it's not hanging there is just one master node; the node itself
         else
         {
           // Set the number of master nodes to one
           n_master = 1;
         }
  
         // Loop over the number of master nodes
         for (unsigned m = 0; m < n_master; m++)
         {
           // Check if the node is hanging
           if (is_node_hanging)
           {
             // Read out the local equation from the master node
             local_eqn = this->local_hang_eqn(hang_info_pt->master_node_pt(m),
                                              u_nodal_index);
  
             // Read out the weight from the master node
             hang_weight = hang_info_pt->master_weight(m);
           }
           // If the node is not hanging
           else
           {
             // The local equation number comes from the node itself
             local_eqn = this->nodal_local_eqn(l, u_nodal_index);
  
             // The hang weight is one
             hang_weight = 1.0;
           }
  
           // If the nodal equation is not a boundary condition
           if (local_eqn >= 0)
           {
             // Add source term and time derivative
             residuals[local_eqn] +=
               ((source + alpha_local * interpolated_dudt) * test(l) * W *
                hang_weight);
  
             // If ALE is enabled
             if (!(this->ALE_is_disabled))
             {
               // Loop over the coordinate directions
               for (unsigned k = 0; k < SPATIAL_DIM; k++)
               {
                 // Add in the mesh velocity contribution
                 residuals[local_eqn] -=
                   (alpha_local * mesh_velocity[k] * interpolated_dudx[k] *
                    test(l) * W * hang_weight);
               }
             } // if (!ALE_is_disabled)
  
             // Loop over the coordinate directions
             for (unsigned k = 0; k < SPATIAL_DIM; k++)
             {
               // Add in the contribution from the Laplace operator
               residuals[local_eqn] += (beta_local * interpolated_dudx[k] *
                                        dtestdx(l, k) * W * hang_weight);
             }
  
             //-----------------------
             // Calculate the Jacobian
             //-----------------------
             // If we also need to construct the Jacobian
             if (flag)
             {
               // Storage for the number of master nodes
               unsigned n_master2 = 1;
  
               // Storage for the hang weight associated with the shape function
               double hang_weight2 = 1.0;
  
               // Loop over the nodes for the variables
               for (unsigned l2 = 0; l2 < n_node; l2++)
               {
                 // Check if the node is hanging
                 bool is_node2_hanging = this->node_pt(l2)->is_hanging();
  
                 // If the node is hanging, get the number of master nodes
                 if (is_node2_hanging)
                 {
                   // Get the hang info pointer associated with the l2-th node
                   hang_info2_pt = this->node_pt(l2)->hanging_pt();
  
                   // Get the number of master nodes associated with the node
                   n_master2 = hang_info2_pt->nmaster();
                 }
                 // If it's not hanging there is just one master node; the node
                 // itself
                 else
                 {
                   // Set the number of master nodes to one
                   n_master2 = 1;
                 }
  
                 // Loop over the master nodes
                 for (unsigned m2 = 0; m2 < n_master2; m2++)
                 {
                   // Check if the node is hanging
                   if (is_node2_hanging)
                   {
                     // Read out the local equation from the master node
                     local_unknown = this->local_hang_eqn(
                       hang_info2_pt->master_node_pt(m2), u_nodal_index);
  
                     // Read out the weight from the master node
                     hang_weight2 = hang_info2_pt->master_weight(m2);
                   }
                   // If the node is not hanging
                   else
                   {
                     // The local equation number comes from the node itself
                     local_unknown = this->nodal_local_eqn(l2, u_nodal_index);
  
                     // The hang weight is one
                     hang_weight2 = 1.0;
                   }
  
                   // If the unknown is not pinned
                   if (local_unknown >= 0)
                   {
                     // Time-derivative contribution
                     jacobian(local_eqn, local_unknown) +=
                       (alpha_local * test(l) * dpsidx(l2, SPATIAL_DIM) * W *
                        hang_weight * hang_weight2);
  
                     // Laplace operator contribution
                     for (unsigned k = 0; k < SPATIAL_DIM; k++)
                     {
                       // Add the Laplacian contribution to the elemental
                       // Jacobian
                       jacobian(local_eqn, local_unknown) +=
                         (beta_local * dpsidx(l2, k) * dtestdx(l, k) * W *
                          hang_weight * hang_weight2);
                     }
  
                     // If ALE is enabled
                     if (!(this->ALE_is_disabled))
                     {
                       // Loop over the spatial coordinates
                       for (unsigned k = 0; k < SPATIAL_DIM; k++)
                       {
                         // Add the ALE contribution to the Jacobian
                         jacobian(local_eqn, local_unknown) -=
                           (alpha_local * mesh_velocity[k] * dpsidx(l2, k) *
                            test(l) * W * hang_weight * hang_weight2);
                       }
                     } // if (!(this->ALE_is_disabled))
                   } // if (local_unknown>=0)
                 } // for (unsigned m2=0;m2<n_master;m2++)
               } // for (unsigned l2=0;l2<n_node;l2++)
             } // if (flag)
           } // if (local_eqn>=0)
         } // for (unsigned m=0;m<n_master;m++)
       } // for (unsigned l=0;l<n_node;l++)
     } // for (unsigned ipt=0;ipt<n_intpt;ipt++)
   } // End of fill_in_generic_residual_contribution_ust_heat

References oomph::ALE_is_disabled, alpha, beta, i, J, j, k, m, m2(), oomph::HangInfo::master_node_pt(), oomph::HangInfo::master_weight(), oomph::HangInfo::nmaster(), s, TestProblem::source(), Eigen::test, w, and oomph::QuadTreeNames::W.

◆ further_build()

template<unsigned SPATIAL_DIM>

void oomph::RefineableSpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::further_build ( )

inlinevirtual

Further build: Copy source function pointer from father element.

Reimplemented from oomph::RefineableElement.

     {
       // Get pointer to the father
       RefineableSpaceTimeUnsteadyHeatMixedOrderEquations<SPATIAL_DIM>*
         cast_father_element_pt = dynamic_cast<
           RefineableSpaceTimeUnsteadyHeatMixedOrderEquations<SPATIAL_DIM>*>(
           this->father_element_pt());
  
       // Get the source function from the parent and store it
       this->Source_fct_pt = cast_father_element_pt->source_fct_pt();
  
       // Set the ALE status from the father
       this->ALE_is_disabled = cast_father_element_pt->ALE_is_disabled;
     } // End of further_build

References oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::ALE_is_disabled, oomph::RefineableElement::father_element_pt(), oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::source_fct_pt(), and oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::Source_fct_pt.

◆ get_interpolated_values() [1/2]

template<unsigned SPATIAL_DIM>

void oomph::RefineableSpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::get_interpolated_values	(	const unsigned &	t,
		const Vector< double > &	s,
		Vector< double > &	values
	)

inlinevirtual

Get the function value u in Vector. Note: Given the generality of the interface (this function is usually called from black-box documentation or interpolation routines), the values Vector sets its own size in here.

Implements oomph::RefineableElement.

     {
       // Set the size of the vector u
       values.resize(1);
  
       // Find the number of nodes
       unsigned n_node = nnode();
  
       // Find the nodal index at which the unknown is stored
       unsigned u_nodal_index = this->u_index_ust_heat();
  
       // Local shape function
       Shape psi(n_node);
  
       // Find values of shape function
       shape(s, psi);
  
       // Initialise the value of u
       values[0] = 0.0;
  
       // Loop over the local nodes and sum
       for (unsigned l = 0; l < n_node; l++)
       {
         // Update the solution value
         values[0] += this->nodal_value(t, l, u_nodal_index) * psi[l];
       }
     } // End of get_interpolated_values

References oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_value(), s, oomph::FiniteElement::shape(), and oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::u_index_ust_heat().

◆ get_interpolated_values() [2/2]

template<unsigned SPATIAL_DIM>

void oomph::RefineableSpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::get_interpolated_values	(	const Vector< double > &	s,
		Vector< double > &	values
	)

inlinevirtual

Get the function value u in Vector. Note: Given the generality of the interface (this function is usually called from black-box documentation or interpolation routines), the values Vector sets its own size in here.

Reimplemented from oomph::RefineableElement.

     {
       // Set the size of the vector u
       values.resize(1);
  
       // Find the number of nodes
       unsigned n_node = nnode();
  
       // Find the nodal index at which the unknown is stored
       unsigned u_nodal_index = this->u_index_ust_heat();
  
       // Local shape function
       Shape psi(n_node);
  
       // Find values of shape function
       shape(s, psi);
  
       // Initialise the value of u
       values[0] = 0.0;
  
       // Loop over the local nodes and sum
       for (unsigned l = 0; l < n_node; l++)
       {
         // Update the solution value
         values[0] += this->nodal_value(l, u_nodal_index) * psi[l];
       }
     } // End of get_interpolated_values

References oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_value(), s, oomph::FiniteElement::shape(), and oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::u_index_ust_heat().

◆ get_Z2_flux()

template<unsigned SPATIAL_DIM>

void oomph::RefineableSpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::get_Z2_flux	(	const Vector< double > &	s,
		Vector< double > &	flux
	)

inlinevirtual

Get 'flux' for Z2 error recovery: Different to the get_flux function in the base class as we also have to include du/dt as we're doing temporal adaptivity too

Implements oomph::ElementWithZ2ErrorEstimator.

     {
       // Find out how many nodes there are in the element
       unsigned n_node = nnode();
  
       // Find the index at which the variable is stored
       unsigned u_nodal_index = this->u_index_ust_heat();
  
       // Set up memory for the shape and test functions
       Shape psi(n_node);
  
       // Set up memory for the derivatives of the shape and test functions
       DShape dpsidx(n_node, SPATIAL_DIM + 1);
  
       // Call the derivatives of the shape and test functions
       dshape_eulerian(s, psi, dpsidx);
  
       // Loop over the entries of the flux vector
       for (unsigned j = 0; j < SPATIAL_DIM + 1; j++)
       {
         // Initialise j-th flux entry to zero
         flux[j] = 0.0;
       }
  
       // Loop over nodes
       for (unsigned l = 0; l < n_node; l++)
       {
         // Loop over derivative directions
         for (unsigned j = 0; j < SPATIAL_DIM + 1; j++)
         {
           // Update the flux value
           flux[j] += this->nodal_value(l, u_nodal_index) * dpsidx(l, j);
         }
       } // for (unsigned l=0;l<n_node;l++)
     } // End of get_Z2_flux

References oomph::FiniteElement::dshape_eulerian(), ProblemParameters::flux(), j, oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_value(), s, and oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::u_index_ust_heat().

◆ num_Z2_flux_terms()

template<unsigned SPATIAL_DIM>

unsigned oomph::RefineableSpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::num_Z2_flux_terms ( )

inlinevirtual

Number of 'flux' terms for Z2 error estimation.

Implements oomph::ElementWithZ2ErrorEstimator.

     {
       // The flux terms are associated with spatial AND temporal derivatives
       return SPATIAL_DIM + 1;
     } // End of num_Z2_flux_terms

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

Public Member Functions

Private Member Functions

Additional Inherited Members

Detailed Description

template<unsigned SPATIAL_DIM> class oomph::RefineableSpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >

Constructor & Destructor Documentation

◆ RefineableSpaceTimeUnsteadyHeatMixedOrderEquations() [1/2]

◆ RefineableSpaceTimeUnsteadyHeatMixedOrderEquations() [2/2]

Member Function Documentation

◆ fill_in_generic_residual_contribution_ust_heat()

◆ further_build()

◆ get_interpolated_values() [1/2]

◆ get_interpolated_values() [2/2]

◆ get_Z2_flux()

◆ num_Z2_flux_terms()

template<unsigned SPATIAL_DIM>
class oomph::RefineableSpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >