#include <navier_stokes_elements.h>

Inheritance diagram for oomph::QTaylorHoodElement< DIM >:

Public Member Functions
	QTaylorHoodElement ()
	Constructor, no internal data points. More...

virtual unsigned	required_nvalue (const unsigned &n) const

void	pshape_nst (const Vector< double > &s, Shape &psi) const
	Pressure shape functions at local coordinate s. More...

void	pshape_nst (const Vector< double > &s, Shape &psi, Shape &test) const
	Pressure shape and test functions at local coordinte s. More...

virtual int	p_nodal_index_nst () const
	Set the value at which the pressure is stored in the nodes. More...

int	p_local_eqn (const unsigned &n) const
	Return the local equation numbers for the pressure values. More...

double	p_nst (const unsigned &n_p) const

double	p_nst (const unsigned &t, const unsigned &n_p) const

double	dpshape_and_dptest_eulerian_nst (const Vector< double > &s, Shape &ppsi, DShape &dppsidx, Shape &ptest, DShape &dptestdx) const

unsigned	npres_nst () const
	Return number of pressure values. More...

bool	is_pressure_node (const unsigned &n) const
	Deduce whether or not the provided node is a pressure node. More...

void	fix_pressure (const unsigned &p_dof, const double &p_value)
	Pin p_dof-th pressure dof and set it to value specified by p_value. More...

void	build_fp_press_adv_diff_robin_bc_element (const unsigned &face_index)

void	identify_load_data (std::set< std::pair< Data *, unsigned >> &paired_load_data)

void	identify_pressure_data (std::set< std::pair< Data *, unsigned >> &paired_pressure_data)

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

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

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

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

unsigned	ndof_types () const

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

double	dpshape_and_dptest_eulerian_nst (const Vector< double > &s, Shape &ppsi, DShape &dppsidx, Shape &ptest, DShape &dptestdx) const

void	pshape_nst (const Vector< double > &s, Shape &psi) const

double	dpshape_and_dptest_eulerian_nst (const Vector< double > &s, Shape &ppsi, DShape &dppsidx, Shape &ptest, DShape &dptestdx) const

void	pshape_nst (const Vector< double > &s, Shape &psi) const

Public Member Functions inherited from oomph::NavierStokesEquations< DIM >
	NavierStokesEquations ()

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

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

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

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

const double &	viscosity_ratio () const

double *&	viscosity_ratio_pt ()
	Pointer to Viscosity Ratio. More...

const double &	density_ratio () const

double *&	density_ratio_pt ()
	Pointer to Density ratio. More...

const double &	re_invfr () const
	Global inverse Froude number. More...

double *&	re_invfr_pt ()
	Pointer to global inverse Froude number. More...

const Vector< double > &	g () const
	Vector of gravitational components. More...

Vector< double > *&	g_pt ()
	Pointer to Vector of gravitational components. More...

NavierStokesBodyForceFctPt &	body_force_fct_pt ()
	Access function for the body-force pointer. More...

NavierStokesBodyForceFctPt	body_force_fct_pt () const
	Access function for the body-force pointer. Const version. More...

NavierStokesSourceFctPt &	source_fct_pt ()
	Access function for the source-function pointer. More...

NavierStokesSourceFctPt	source_fct_pt () const
	Access function for the source-function pointer. Const version. More...

NavierStokesPressureAdvDiffSourceFctPt &	source_fct_for_pressure_adv_diff ()

NavierStokesPressureAdvDiffSourceFctPt	source_fct_for_pressure_adv_diff () const

int &	pinned_fp_pressure_eqn ()

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

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

virtual unsigned	u_index_nst (const unsigned &i) const

unsigned	n_u_nst () const

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

void	disable_ALE ()

void	enable_ALE ()

double	pressure_integral () const
	Integral of pressure over element. More...

double	dissipation () const
	Return integral of dissipation over element. More...

double	dissipation (const Vector< double > &s) const
	Return dissipation at local coordinate s. More...

void	get_vorticity (const Vector< double > &s, Vector< double > &vorticity) const
	Compute the vorticity vector at local coordinate s. More...

void	get_vorticity (const Vector< double > &s, double &vorticity) const
	Compute the scalar vorticity at local coordinate s (2D) More...

double	kin_energy () const
	Get integral of kinetic energy over element. More...

double	d_kin_energy_dt () const
	Get integral of time derivative of kinetic energy over element. More...

void	strain_rate (const Vector< double > &s, DenseMatrix< double > &strain_rate) const
	Strain-rate tensor: 1/2 (du_i/dx_j + du_j/dx_i) More...

void	get_traction (const Vector< double > &s, const Vector< double > &N, Vector< double > &traction)

void	get_traction (const Vector< double > &s, const Vector< double > &N, Vector< double > &traction_p, Vector< double > &traction_visc_n, Vector< double > &traction_visc_t)

void	get_load (const Vector< double > &s, const Vector< double > &N, Vector< double > &load)

void	get_pressure_and_velocity_mass_matrix_diagonal (Vector< double > &press_mass_diag, Vector< double > &veloc_mass_diag, const unsigned &which_one=0)

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, const double &time, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt) const

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

void	full_output (std::ostream &outfile)

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

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

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

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

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

void	compute_norm (double &norm)
	Compute norm of solution: square of the L2 norm of the velocities. More...

void	compute_norm (Vector< double > &norm)
	Compute the vector norm of the FEM solution. More...

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

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

void	compute_error (FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, double &norm)

void	compute_error (FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)

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

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

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

void	fill_in_contribution_to_dresiduals_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam)
	Compute the element's residual Vector. More...

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

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)

void	fill_in_pressure_advection_diffusion_residuals (Vector< double > &residuals)

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

void	pin_all_non_pressure_dofs (std::map< Data *, std::vector< int >> &eqn_number_backup)
	Pin all non-pressure dofs and backup eqn numbers. More...

void	output_pressure_advection_diffusion_robin_elements (std::ostream &outfile)

void	delete_pressure_advection_diffusion_robin_elements ()

virtual void	get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates)

void	interpolated_u_nst (const Vector< double > &s, Vector< double > &veloc) const
	Compute vector of FE interpolated velocity u at local coordinate s. More...

double	interpolated_u_nst (const Vector< double > &s, const unsigned &i) const
	Return FE interpolated velocity u[i] at local coordinate s. More...

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

virtual void	dinterpolated_u_nst_ddata (const Vector< double > &s, const unsigned &i, Vector< double > &du_ddata, Vector< unsigned > &global_eqn_number)

virtual double	interpolated_p_nst (const Vector< double > &s) const
	Return FE interpolated pressure at local coordinate s. More...

double	interpolated_p_nst (const unsigned &t, const Vector< double > &s) const
	Return FE interpolated pressure at local coordinate s at time level t. More...

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

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

void	get_vorticity (const Vector< double > &s, Vector< double > &vorticity) const

void	get_vorticity (const Vector< double > &s, double &vorticity) const

void	get_vorticity (const Vector< double > &s, Vector< double > &vorticity) const
	Compute 3D vorticity vector at local coordinate s. More...

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

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

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

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

void	set_nodal_dimension (const unsigned &nodal_dim)

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

void	set_n_node (const unsigned &n)

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

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

	FiniteElement ()
	Constructor. More...

virtual	~FiniteElement ()

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

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

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

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

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

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

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

virtual void	set_macro_elem_pt (MacroElement *macro_elem_pt)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

virtual double	J_eulerian_at_knot (const unsigned &ipt) const

void	check_J_eulerian_at_knots (bool &passed) const

void	check_jacobian (const double &jacobian) const

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

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

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

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

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

virtual void	assign_nodal_local_eqn_numbers (const bool &store_local_dof_pt)

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

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

virtual void	assign_all_generic_local_eqn_numbers (const bool &store_local_dof_pt)

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

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

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

virtual unsigned	nnode_1d () const

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 unsigned	nvertex_node () const

virtual Node *	vertex_node_pt (const unsigned &j) const

virtual Node *	construct_node (const unsigned &n)

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

virtual Node *	construct_boundary_node (const unsigned &n)

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

int	get_node_number (Node *const &node_pt) const

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

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

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

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

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

unsigned	dim () const

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

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

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

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

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

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

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

unsigned	ngeom_data () const

Data *	geom_data_pt (const unsigned &j)

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

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

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

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

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

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

virtual void	node_update ()

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

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

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

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

double	size () const

virtual double	compute_physical_size () const

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

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)

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::TemplateFreeNavierStokesEquationsBase
	TemplateFreeNavierStokesEquationsBase ()
	Constructor (empty) More...

virtual	~TemplateFreeNavierStokesEquationsBase ()
	Virtual destructor (empty) More...

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

virtual	~NavierStokesElementWithDiagonalMassMatrices ()
	Virtual destructor. More...

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

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

Protected Member Functions
double	dshape_and_dtest_eulerian_nst (const Vector< double > &s, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const

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

double	dshape_and_dtest_eulerian_at_knot_nst (const unsigned &ipt, Shape &psi, DShape &dpsidx, RankFourTensor< double > &d_dpsidx_dX, Shape &test, DShape &dtestdx, RankFourTensor< double > &d_dtestdx_dX, DenseMatrix< double > &djacobian_dX) const

const unsigned	Pconv [4]

const unsigned	Pconv [8]

double	dshape_and_dtest_eulerian_at_knot_nst (const unsigned &ipt, Shape &psi, DShape &dpsidx, RankFourTensor< double > &d_dpsidx_dX, Shape &test, DShape &dtestdx, RankFourTensor< double > &d_dtestdx_dX, DenseMatrix< double > &djacobian_dX) const

double	dshape_and_dtest_eulerian_at_knot_nst (const unsigned &ipt, Shape &psi, DShape &dpsidx, RankFourTensor< double > &d_dpsidx_dX, Shape &test, DShape &dtestdx, RankFourTensor< double > &d_dtestdx_dX, DenseMatrix< double > &djacobian_dX) const

Protected Member Functions inherited from oomph::NavierStokesEquations< DIM >
virtual void	get_body_force_nst (const double &time, const unsigned &ipt, const Vector< double > &s, const Vector< double > &x, Vector< double > &result)

virtual void	get_body_force_gradient_nst (const double &time, const unsigned &ipt, const Vector< double > &s, const Vector< double > &x, DenseMatrix< double > &d_body_force_dx)

virtual double	get_source_nst (const double &time, const unsigned &ipt, const Vector< double > &x)

virtual void	get_source_gradient_nst (const double &time, const unsigned &ipt, const Vector< double > &x, Vector< double > &gradient)

virtual void	fill_in_generic_residual_contribution_nst (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix, unsigned flag)

virtual void	fill_in_generic_pressure_advection_diffusion_contribution_nst (Vector< double > &residuals, DenseMatrix< double > &jacobian, unsigned flag)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

void	fill_in_jacobian_from_nodal_by_fd (DenseMatrix< double > &jacobian)

virtual void	update_before_nodal_fd ()

virtual void	reset_after_nodal_fd ()

virtual void	update_in_nodal_fd (const unsigned &i)

virtual void	reset_in_nodal_fd (const unsigned &i)

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_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)

Static Protected Attributes
static const unsigned	Pconv []

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

Private Member Functions
const unsigned	Initial_Nvalue [9]

const unsigned	Initial_Nvalue [27]

Static Private Attributes
static const unsigned	Initial_Nvalue []
	Static array of ints to hold number of variables at node. More...

Additional Inherited Members
Public Types inherited from oomph::NavierStokesEquations< DIM >
typedef void(*	NavierStokesBodyForceFctPt) (const double &time, const Vector< double > &x, Vector< double > &body_force)

typedef double(*	NavierStokesSourceFctPt) (const double &time, const Vector< double > &x)

typedef double(*	NavierStokesPressureAdvDiffSourceFctPt) (const Vector< double > &x)

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 Attributes inherited from oomph::NavierStokesEquations< DIM >
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 Attributes inherited from oomph::NavierStokesEquations< DIM >
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 *	ReInvFr_pt

Vector< double > *	G_pt
	Pointer to global gravity Vector. More...

NavierStokesBodyForceFctPt	Body_force_fct_pt
	Pointer to body force function. More...

NavierStokesSourceFctPt	Source_fct_pt
	Pointer to volumetric source function. More...

NavierStokesPressureAdvDiffSourceFctPt	Press_adv_diff_source_fct_pt

bool	ALE_is_disabled

Vector< FpPressureAdvDiffRobinBCElementBase * >	Pressure_advection_diffusion_robin_element_pt

int	Pinned_fp_pressure_eqn

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

Detailed Description

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

///////////////////////////////////////////////////////////////////////// ///////////////////////////////////////////////////////////////////////// Taylor–Hood elements are Navier–Stokes elements with quadratic interpolation for velocities and positions and continuous linear pressure interpolation. They can be used within oomph-lib's block-preconditioning framework.

Constructor & Destructor Documentation

◆ QTaylorHoodElement()

template<unsigned DIM>

oomph::QTaylorHoodElement< DIM >::QTaylorHoodElement ( )

inline

Constructor, no internal data points.

2351 : QElement<DIM, 3>(), NavierStokesEquations<DIM>() {}

QElement

Member Function Documentation

◆ build_fp_press_adv_diff_robin_bc_element()

template<unsigned DIM>

void oomph::QTaylorHoodElement< DIM >::build_fp_press_adv_diff_robin_bc_element ( const unsigned & face_index )

inlinevirtual

Build FaceElements that apply the Robin boundary condition to the pressure advection diffusion problem required by Fp preconditioner

Implements oomph::NavierStokesEquations< DIM >.

Reimplemented in oomph::RefineableQTaylorHoodElement< DIM >, and oomph::RefineableQTaylorHoodElement< 2 >.

     {
       this->Pressure_advection_diffusion_robin_element_pt.push_back(
         new FpPressureAdvDiffRobinBCElement<QTaylorHoodElement<DIM>>(
           this, face_index));
     }

References oomph::NavierStokesEquations< DIM >::Pressure_advection_diffusion_robin_element_pt.

◆ dpshape_and_dptest_eulerian_nst() [1/3]

template<unsigned DIM>

double oomph::QTaylorHoodElement< DIM >::dpshape_and_dptest_eulerian_nst	(	const Vector< double > &	s,
		Shape &	ppsi,
		DShape &	dppsidx,
		Shape &	ptest,
		DShape &	dptestdx
	)		const

inlinevirtual

Pressure shape and test functions and their derivs w.r.t. to global coords at local coordinate s (taken from geometry). Return Jacobian of mapping between local and global coordinates.

Implements oomph::NavierStokesEquations< DIM >.

◆ dpshape_and_dptest_eulerian_nst() [2/3]

double oomph::QTaylorHoodElement< 2 >::dpshape_and_dptest_eulerian_nst	(	const Vector< double > &	s,
		Shape &	ppsi,
		DShape &	dppsidx,
		Shape &	ptest,
		DShape &	dptestdx
	)		const

inlinevirtual

2D : Pressure shape and test functions and derivs w.r.t. to Eulerian coords. Return Jacobian of mapping between local and global coordinates.

Implements oomph::NavierStokesEquations< DIM >.

   {
     // Local storage
     double psi1[2], psi2[2];
     double dpsi1[2], dpsi2[2];
  
     // Call the OneDimensional Shape functions
     OneDimLagrange::shape<2>(s[0], psi1);
     OneDimLagrange::shape<2>(s[1], psi2);
     OneDimLagrange::dshape<2>(s[0], dpsi1);
     OneDimLagrange::dshape<2>(s[1], dpsi2);
  
     // Now let's loop over the nodal points in the element
     // s1 is the "x" coordinate, s2 the "y"
     for (unsigned i = 0; i < 2; i++)
     {
       for (unsigned j = 0; j < 2; j++)
       {
         /*Multiply the two 1D functions together to get the 2D function*/
         ppsi[2 * i + j] = psi2[i] * psi1[j];
         dppsidx(2 * i + j, 0) = psi2[i] * dpsi1[j];
         dppsidx(2 * i + j, 1) = dpsi2[i] * psi1[j];
       }
     }
  
  
     // Get the values of the shape functions and their local derivatives
     Shape psi(9);
     DShape dpsi(9, 2);
     dshape_local(s, psi, dpsi);
  
     // Allocate memory for the inverse 2x2 jacobian
     DenseMatrix<double> inverse_jacobian(2);
  
     // Now calculate the inverse jacobian
     const double det = local_to_eulerian_mapping(dpsi, inverse_jacobian);
  
     // Now set the values of the derivatives to be derivs w.r.t. to the
     // Eulerian coordinates
     transform_derivatives(inverse_jacobian, dppsidx);
  
     // The test functions are equal to the shape functions
     ptest = ppsi;
     dptestdx = dppsidx;
  
     // Return the determinant of the jacobian
     return det;
   }

References oomph::OneDimLagrange::dshape< 2 >(), i, j, s, and oomph::OneDimLagrange::shape< 2 >().

◆ dpshape_and_dptest_eulerian_nst() [3/3]

double oomph::QTaylorHoodElement< 3 >::dpshape_and_dptest_eulerian_nst	(	const Vector< double > &	s,
		Shape &	ppsi,
		DShape &	dppsidx,
		Shape &	ptest,
		DShape &	dptestdx
	)		const

inlinevirtual

3D : Pressure shape and test functions and derivs w.r.t. to Eulerian coords. Return Jacobian of mapping between local and global coordinates.

Implements oomph::NavierStokesEquations< DIM >.

   {
     // Local storage
     double psi1[2], psi2[2], psi3[2];
     double dpsi1[2], dpsi2[2], dpsi3[2];
  
     // Call the OneDimensional Shape functions
     OneDimLagrange::shape<2>(s[0], psi1);
     OneDimLagrange::shape<2>(s[1], psi2);
     OneDimLagrange::shape<2>(s[2], psi3);
     OneDimLagrange::dshape<2>(s[0], dpsi1);
     OneDimLagrange::dshape<2>(s[1], dpsi2);
     OneDimLagrange::dshape<2>(s[2], dpsi3);
  
     // Now let's loop over the nodal points in the element
     // s0 is the "x" coordinate, s1 the "y", s2 is the "z"
     for (unsigned i = 0; i < 2; i++)
     {
       for (unsigned j = 0; j < 2; j++)
       {
         for (unsigned k = 0; k < 2; k++)
         {
           /*Multiply the three 1D functions together to get the 3D function*/
           ppsi[4 * i + 2 * j + k] = psi3[i] * psi2[j] * psi1[k];
           dppsidx(4 * i + 2 * j + k, 0) = psi3[i] * psi2[j] * dpsi1[k];
           dppsidx(4 * i + 2 * j + k, 1) = psi3[i] * dpsi2[j] * psi1[k];
           dppsidx(4 * i + 2 * j + k, 2) = dpsi3[i] * psi2[j] * psi1[k];
         }
       }
     }
  
  
     // Get the values of the shape functions and their local derivatives
     Shape psi(27);
     DShape dpsi(27, 3);
     dshape_local(s, psi, dpsi);
  
     // Allocate memory for the inverse 3x3 jacobian
     DenseMatrix<double> inverse_jacobian(3);
  
     // Now calculate the inverse jacobian
     const double det = local_to_eulerian_mapping(dpsi, inverse_jacobian);
  
     // Now set the values of the derivatives to be derivs w.r.t. to the
     // Eulerian coordinates
     transform_derivatives(inverse_jacobian, dppsidx);
  
     // The test functions are equal to the shape functions
     ptest = ppsi;
     dptestdx = dppsidx;
  
     // Return the determinant of the jacobian
     return det;
   }

References oomph::OneDimLagrange::dshape< 2 >(), i, j, k, s, and oomph::OneDimLagrange::shape< 2 >().

◆ dshape_and_dtest_eulerian_at_knot_nst() [1/4]

template<unsigned DIM>

double oomph::QTaylorHoodElement< DIM >::dshape_and_dtest_eulerian_at_knot_nst	(	const unsigned &	ipt,
		Shape &	psi,
		DShape &	dpsidx,
		RankFourTensor< double > &	d_dpsidx_dX,
		Shape &	test,
		DShape &	dtestdx,
		RankFourTensor< double > &	d_dtestdx_dX,
		DenseMatrix< double > &	djacobian_dX
	)		const

inlineprotectedvirtual

Shape/test functions and derivs w.r.t. to global coords at integration point ipt; return Jacobian of mapping (J). Also compute derivatives of dpsidx, dtestdx and J w.r.t. nodal coordinates.

Implements oomph::NavierStokesEquations< DIM >.

◆ dshape_and_dtest_eulerian_at_knot_nst() [2/4]

double oomph::QTaylorHoodElement< 2 >::dshape_and_dtest_eulerian_at_knot_nst	(	const unsigned &	ipt,
		Shape &	psi,
		DShape &	dpsidx,
		RankFourTensor< double > &	d_dpsidx_dX,
		Shape &	test,
		DShape &	dtestdx,
		RankFourTensor< double > &	d_dtestdx_dX,
		DenseMatrix< double > &	djacobian_dX
	)		const

inlineprotectedvirtual

2D : Define the shape functions (psi) and test functions (test) and their derivatives w.r.t. global coordinates (dpsidx and dtestdx) and return Jacobian of mapping (J). Additionally compute the derivatives of dpsidx, dtestdx and J w.r.t. nodal coordinates.

Galerkin: Test functions = shape functions

Implements oomph::NavierStokesEquations< DIM >.

   {
     // Call the geometrical shape functions and derivatives
     const double J = this->dshape_eulerian_at_knot(
       ipt, psi, dpsidx, djacobian_dX, d_dpsidx_dX);
  
     // Loop over the test functions and derivatives and set them equal to the
     // shape functions
     for (unsigned i = 0; i < 9; i++)
     {
       test[i] = psi[i];
  
       for (unsigned k = 0; k < 2; k++)
       {
         dtestdx(i, k) = dpsidx(i, k);
  
         for (unsigned p = 0; p < 2; p++)
         {
           for (unsigned q = 0; q < 9; q++)
           {
             d_dtestdx_dX(p, q, i, k) = d_dpsidx_dX(p, q, i, k);
           }
         }
       }
     }
  
     // Return the jacobian
     return J;
   }

References i, J, k, p, and Eigen::numext::q.

◆ dshape_and_dtest_eulerian_at_knot_nst() [3/4]

double oomph::QTaylorHoodElement< 3 >::dshape_and_dtest_eulerian_at_knot_nst	(	const unsigned &	ipt,
		Shape &	psi,
		DShape &	dpsidx,
		RankFourTensor< double > &	d_dpsidx_dX,
		Shape &	test,
		DShape &	dtestdx,
		RankFourTensor< double > &	d_dtestdx_dX,
		DenseMatrix< double > &	djacobian_dX
	)		const

inlineprotectedvirtual

3D : Define the shape functions (psi) and test functions (test) and their derivatives w.r.t. global coordinates (dpsidx and dtestdx) and return Jacobian of mapping (J). Additionally compute the derivatives of dpsidx, dtestdx and J w.r.t. nodal coordinates.

Galerkin: Test functions = shape functions

Implements oomph::NavierStokesEquations< DIM >.

   {
     // Call the geometrical shape functions and derivatives
     const double J = this->dshape_eulerian_at_knot(
       ipt, psi, dpsidx, djacobian_dX, d_dpsidx_dX);
  
     // Loop over the test functions and derivatives and set them equal to the
     // shape functions
     for (unsigned i = 0; i < 27; i++)
     {
       test[i] = psi[i];
  
       for (unsigned k = 0; k < 3; k++)
       {
         dtestdx(i, k) = dpsidx(i, k);
  
         for (unsigned p = 0; p < 3; p++)
         {
           for (unsigned q = 0; q < 27; q++)
           {
             d_dtestdx_dX(p, q, i, k) = d_dpsidx_dX(p, q, i, k);
           }
         }
       }
     }
  
     // Return the jacobian
     return J;
   }

References i, J, k, p, and Eigen::numext::q.

◆ dshape_and_dtest_eulerian_at_knot_nst() [4/4]

template<unsigned DIM>

double oomph::QTaylorHoodElement< DIM >::dshape_and_dtest_eulerian_at_knot_nst	(	const unsigned &	ipt,
		Shape &	psi,
		DShape &	dpsidx,
		Shape &	test,
		DShape &	dtestdx
	)		const

inlineprotectedvirtual

Velocity shape and test functions and their derivs w.r.t. to global coords at local coordinate s (taken from geometry) Return Jacobian of mapping between local and global coordinates.

Derivatives of the shape functions and test functions w.r.t to global (Eulerian) coordinates. Return Jacobian of mapping between local and global coordinates.

Implements oomph::NavierStokesEquations< DIM >.

   {
     // Call the geometrical shape functions and derivatives
     double J = this->dshape_eulerian_at_knot(ipt, psi, dpsidx);
  
     // The test functions are equal to the shape functions
     test = psi;
     dtestdx = dpsidx;
  
     // Return the jacobian
     return J;
   }

References J.

◆ dshape_and_dtest_eulerian_nst()

template<unsigned DIM>

double oomph::QTaylorHoodElement< DIM >::dshape_and_dtest_eulerian_nst	(	const Vector< double > &	s,
		Shape &	psi,
		DShape &	dpsidx,
		Shape &	test,
		DShape &	dtestdx
	)		const

inlineprotectedvirtual

Velocity shape and test functions and their derivs w.r.t. to global coords at local coordinate s (taken from geometry) Return Jacobian of mapping between local and global coordinates.

Derivatives of the shape functions and test functions w.r.t to global (Eulerian) coordinates. Return Jacobian of mapping between local and global coordinates.

Implements oomph::NavierStokesEquations< DIM >.

   {
     // Call the geometrical shape functions and derivatives
     double J = this->dshape_eulerian(s, psi, dpsidx);
  
     // The test functions are equal to the shape functions
     test = psi;
     dtestdx = dpsidx;
  
     // Return the jacobian
     return J;
   }

References J, and s.

◆ fix_pressure()

template<unsigned DIM>

void oomph::QTaylorHoodElement< DIM >::fix_pressure	(	const unsigned &	p_dof,
		const double &	p_value
	)

inlinevirtual

Pin p_dof-th pressure dof and set it to value specified by p_value.

Implements oomph::NavierStokesEquations< DIM >.

     {
       this->node_pt(Pconv[p_dof])->pin(this->p_nodal_index_nst());
       this->node_pt(Pconv[p_dof])
         ->set_value(this->p_nodal_index_nst(), p_value);
     }

References oomph::FiniteElement::node_pt(), oomph::QTaylorHoodElement< DIM >::p_nodal_index_nst(), oomph::Data::pin(), and oomph::Data::set_value().

◆ get_dof_numbers_for_unknowns()

template<unsigned DIM>

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

virtual

Create a list of pairs for all unknowns in this element, so that the first entry in each pair contains the global equation number of the unknown, while the second one contains the number of the "DOF type" that this unknown is associated with. (Function can obviously only be called if the equation numbering scheme has been set up.) Velocity=0; Pressure=1

Create a list of pairs for all unknowns in this element, so the first entry in each pair contains the global equation number of the unknown, while the second one contains the number of the "DOF type" that this unknown is associated with. (Function can obviously only be called if the equation numbering scheme has been set up.)

Reimplemented from oomph::GeneralisedElement.

   {
     // number of nodes
     unsigned n_node = this->nnode();
  
     // local eqn no for pressure unknown
     // unsigned p_index = this->p_nodal_index_nst();
  
     // temporary pair (used to store dof lookup prior to being added to list)
     std::pair<unsigned, unsigned> dof_lookup;
  
     // loop over the nodes
     for (unsigned n = 0; n < n_node; n++)
     {
       // find the number of values at this node
       unsigned nv = this->required_nvalue(n);
  
       // loop over these values
       for (unsigned v = 0; v < nv; v++)
       {
         // determine local eqn number
         int local_eqn_number = this->nodal_local_eqn(n, v);
  
         // ignore pinned values - far away degrees of freedom resulting
         // from hanging nodes can be ignored since these are be dealt
         // with by the element containing their master nodes
         if (local_eqn_number >= 0)
         {
           // store dof lookup in temporary pair: Global equation number
           // is the first entry in pair
           dof_lookup.first = this->eqn_number(local_eqn_number);
  
           // set dof numbers: Dof number is the second entry in pair
           dof_lookup.second = v;
  
           // add to list
           dof_lookup_list.push_front(dof_lookup);
         }
       }
     }
   }

References n, and v.

◆ identify_load_data()

template<unsigned DIM>

void oomph::QTaylorHoodElement< DIM >::identify_load_data ( std::set< std::pair< Data *, unsigned >> & paired_load_data )

virtual

Add to the set paired_load_data pairs containing

the pointer to a Data object and
the index of the value in that Data object

for all values (pressures, velocities) that affect the load computed in the get_load(...) function.

Implements oomph::FSIFluidElement.

Reimplemented in oomph::RefineableQTaylorHoodElement< DIM >, and oomph::RefineableQTaylorHoodElement< 2 >.

   {
     // Find the index at which the velocity is stored
     unsigned u_index[DIM];
     for (unsigned i = 0; i < DIM; i++)
     {
       u_index[i] = this->u_index_nst(i);
     }
  
     // Loop over the nodes
     unsigned n_node = this->nnode();
     for (unsigned n = 0; n < n_node; n++)
     {
       // Loop over the velocity components and add pointer to their data
       // and indices to the vectors
       for (unsigned i = 0; i < DIM; i++)
       {
         paired_load_data.insert(std::make_pair(this->node_pt(n), u_index[i]));
       }
     }
  
     // Identify the pressure data
     this->identify_pressure_data(paired_load_data);
   }

References DIM, i, and n.

◆ identify_pressure_data()

template<unsigned DIM>

void oomph::QTaylorHoodElement< DIM >::identify_pressure_data ( std::set< std::pair< Data *, unsigned >> & paired_pressure_data )

virtual

Add to the set paired_pressure_data pairs containing

the pointer to a Data object and
the index of the value in that Data object

for all pressure values that affect the load computed in the get_load(...) function.

Add to the set paired_pressure_data pairs containing

the pointer to a Data object and
the index of the value in that Data object

for pressure values that affect the load computed in the get_load(...) function.,

Implements oomph::FSIFluidElement.

   {
     // Find the index at which the pressure is stored
     unsigned p_index = static_cast<unsigned>(this->p_nodal_index_nst());
  
     // Loop over the pressure data
     unsigned n_pres = npres_nst();
     for (unsigned l = 0; l < n_pres; l++)
     {
       // The DIMth entry in each nodal data is the pressure, which
       // affects the traction
       paired_pressure_data.insert(
         std::make_pair(this->node_pt(Pconv[l]), p_index));
     }
   }

◆ Initial_Nvalue() [1/2]

const unsigned oomph::QTaylorHoodElement< 3 >::Initial_Nvalue

private

◆ Initial_Nvalue() [2/2]

const unsigned oomph::QTaylorHoodElement< 2 >::Initial_Nvalue

private

//////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////////

◆ is_pressure_node()

template<unsigned DIM>

bool oomph::QTaylorHoodElement< DIM >::is_pressure_node ( const unsigned & n ) const

inline

Deduce whether or not the provided node is a pressure node.

     {
       // The number of pressure nodes
       unsigned n_p = npres_nst();
  
       // See if the value n is in the array Pconv
       return std::find(this->Pconv, this->Pconv + n_p, n) != this->Pconv + n_p;
     } // End of is_pressure_node

References n, and oomph::QTaylorHoodElement< DIM >::npres_nst().

◆ ndof_types()

template<unsigned DIM>

unsigned oomph::QTaylorHoodElement< DIM >::ndof_types ( ) const

inlinevirtual

Returns the number of "DOF types" that degrees of freedom in this element are sub-divided into: Velocity and pressure.

Reimplemented from oomph::GeneralisedElement.

     {
       return DIM + 1;
     }

References DIM.

◆ npres_nst()

template<unsigned DIM>

unsigned oomph::QTaylorHoodElement< DIM >::npres_nst ( ) const

inlinevirtual

Return number of pressure values.

Implements oomph::NavierStokesEquations< DIM >.

     {
       return static_cast<unsigned>(pow(2.0, static_cast<int>(DIM)));
     }

References DIM, and Eigen::bfloat16_impl::pow().

Referenced by oomph::RefineableQTaylorHoodElement< DIM >::identify_load_data(), oomph::QTaylorHoodElement< DIM >::is_pressure_node(), and oomph::RefineableQTaylorHoodElement< DIM >::pin_elemental_redundant_nodal_pressure_dofs().

◆ output() [1/4]

template<unsigned DIM>

void oomph::QTaylorHoodElement< DIM >::output ( FILE * file_pt )

inlinevirtual

Redirect output to NavierStokesEquations output.

Reimplemented from oomph::NavierStokesEquations< DIM >.

     {
       NavierStokesEquations<DIM>::output(file_pt);
     }

References oomph::NavierStokesEquations< DIM >::output().

◆ output() [2/4]

template<unsigned DIM>

void oomph::QTaylorHoodElement< DIM >::output	(	FILE *	file_pt,
		const unsigned &	nplot
	)

inlinevirtual

Redirect output to NavierStokesEquations output.

Reimplemented from oomph::NavierStokesEquations< DIM >.

     {
       NavierStokesEquations<DIM>::output(file_pt, nplot);
     }

References oomph::NavierStokesEquations< DIM >::output().

◆ output() [3/4]

template<unsigned DIM>

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

inlinevirtual

Redirect output to NavierStokesEquations output.

Reimplemented from oomph::NavierStokesEquations< DIM >.

     {
       NavierStokesEquations<DIM>::output(outfile);
     }

References oomph::NavierStokesEquations< DIM >::output().

◆ output() [4/4]

template<unsigned DIM>

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

inlinevirtual

Redirect output to NavierStokesEquations output.

Reimplemented from oomph::NavierStokesEquations< DIM >.

     {
       NavierStokesEquations<DIM>::output(outfile, nplot);
     }

References oomph::NavierStokesEquations< DIM >::output().

◆ p_local_eqn()

template<unsigned DIM>

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

inlinevirtual

Return the local equation numbers for the pressure values.

Implements oomph::TemplateFreeNavierStokesEquationsBase.

     {
       return this->nodal_local_eqn(Pconv[n], p_nodal_index_nst());
     }

References n, oomph::FiniteElement::nodal_local_eqn(), and oomph::QTaylorHoodElement< DIM >::p_nodal_index_nst().

◆ p_nodal_index_nst()

template<unsigned DIM>

virtual int oomph::QTaylorHoodElement< DIM >::p_nodal_index_nst ( ) const

inlinevirtual

Set the value at which the pressure is stored in the nodes.

Reimplemented from oomph::NavierStokesEquations< DIM >.

     {
       return static_cast<int>(DIM);
     }

References DIM.

Referenced by oomph::QTaylorHoodElement< DIM >::fix_pressure(), oomph::RefineableQTaylorHoodElement< DIM >::further_setup_hanging_nodes(), oomph::RefineableQTaylorHoodElement< DIM >::identify_load_data(), oomph::QTaylorHoodElement< DIM >::p_local_eqn(), oomph::QTaylorHoodElement< DIM >::p_nst(), oomph::RefineableQTaylorHoodElement< DIM >::pin_elemental_redundant_nodal_pressure_dofs(), and oomph::RefineableQTaylorHoodElement< DIM >::unpin_elemental_pressure_dofs().

◆ p_nst() [1/2]

template<unsigned DIM>

double oomph::QTaylorHoodElement< DIM >::p_nst ( const unsigned & n_p ) const

inlinevirtual

Access function for the pressure values at local pressure node n_p (const version)

Implements oomph::NavierStokesEquations< DIM >.

     {
       return this->nodal_value(Pconv[n_p], this->p_nodal_index_nst());
     }

References oomph::FiniteElement::nodal_value(), and oomph::QTaylorHoodElement< DIM >::p_nodal_index_nst().

◆ p_nst() [2/2]

template<unsigned DIM>

double oomph::QTaylorHoodElement< DIM >::p_nst	(	const unsigned &	t,
		const unsigned &	n_p
	)		const

inlinevirtual

Access function for the pressure values at local pressure node n_p (const version)

Implements oomph::NavierStokesEquations< DIM >.

     {
       return this->nodal_value(t, Pconv[n_p], this->p_nodal_index_nst());
     }

References oomph::FiniteElement::nodal_value(), oomph::QTaylorHoodElement< DIM >::p_nodal_index_nst(), and oomph::QTaylorHoodElement< DIM >::Pconv.

◆ Pconv() [1/2]

const unsigned oomph::QTaylorHoodElement< 2 >::Pconv

protected

◆ Pconv() [2/2]

const unsigned oomph::QTaylorHoodElement< 3 >::Pconv

protected

◆ pshape_nst() [1/4]

template<unsigned DIM>

void oomph::QTaylorHoodElement< DIM >::pshape_nst	(	const Vector< double > &	s,
		Shape &	psi
	)		const

inlinevirtual

Pressure shape functions at local coordinate s.

Implements oomph::NavierStokesEquations< DIM >.

Referenced by oomph::RefineableQTaylorHoodElement< DIM >::interpolating_basis().

◆ pshape_nst() [2/4]

void oomph::QTaylorHoodElement< 2 >::pshape_nst	(	const Vector< double > &	s,
		Shape &	psi
	)		const

inlinevirtual

2D : Pressure shape functions

Implements oomph::NavierStokesEquations< DIM >.

   {
     // Local storage
     double psi1[2], psi2[2];
     // Call the OneDimensional Shape functions
     OneDimLagrange::shape<2>(s[0], psi1);
     OneDimLagrange::shape<2>(s[1], psi2);
  
     // Now let's loop over the nodal points in the element
     // s1 is the "x" coordinate, s2 the "y"
     for (unsigned i = 0; i < 2; i++)
     {
       for (unsigned j = 0; j < 2; j++)
       {
         /*Multiply the two 1D functions together to get the 2D function*/
         psi[2 * i + j] = psi2[i] * psi1[j];
       }
     }
   }

References i, j, s, and oomph::OneDimLagrange::shape< 2 >().

◆ pshape_nst() [3/4]

void oomph::QTaylorHoodElement< 3 >::pshape_nst	(	const Vector< double > &	s,
		Shape &	psi
	)		const

inlinevirtual

3D : Pressure shape functions

Implements oomph::NavierStokesEquations< DIM >.

   {
     // Local storage
     double psi1[2], psi2[2], psi3[2];
  
     // Call the OneDimensional Shape functions
     OneDimLagrange::shape<2>(s[0], psi1);
     OneDimLagrange::shape<2>(s[1], psi2);
     OneDimLagrange::shape<2>(s[2], psi3);
  
     // Now let's loop over the nodal points in the element
     // s0 is the "x" coordinate, s1 the "y", s2 is the "z"
     for (unsigned i = 0; i < 2; i++)
     {
       for (unsigned j = 0; j < 2; j++)
       {
         for (unsigned k = 0; k < 2; k++)
         {
           /*Multiply the three 1D functions together to get the 3D function*/
           psi[4 * i + 2 * j + k] = psi3[i] * psi2[j] * psi1[k];
         }
       }
     }
   }

References i, j, k, s, and oomph::OneDimLagrange::shape< 2 >().

◆ pshape_nst() [4/4]

template<unsigned DIM>

void oomph::QTaylorHoodElement< DIM >::pshape_nst	(	const Vector< double > &	s,
		Shape &	psi,
		Shape &	test
	)		const

inlinevirtual

Pressure shape and test functions at local coordinte s.

Pressure shape and test functions.

Implements oomph::NavierStokesEquations< DIM >.

   {
     // Call the pressure shape functions
     this->pshape_nst(s, psi);
     // Test functions are shape functions
     test = psi;
   }

References s.

◆ required_nvalue()

template<unsigned DIM>

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

inlinevirtual

Number of values (pinned or dofs) required at node n. Can be overwritten for hanging node version

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::RefineableQTaylorHoodElement< DIM >, and oomph::RefineableQTaylorHoodElement< 2 >.

     {
       return Initial_Nvalue[n];
     }

References oomph::QTaylorHoodElement< DIM >::Initial_Nvalue, and n.

Member Data Documentation

◆ Initial_Nvalue

template<unsigned DIM>

const unsigned oomph::QTaylorHoodElement< DIM >::Initial_Nvalue[]

staticprivate

Static array of ints to hold number of variables at node.

Referenced by oomph::QTaylorHoodElement< DIM >::required_nvalue().

◆ Pconv

template<unsigned DIM>

const unsigned oomph::QTaylorHoodElement< DIM >::Pconv[]

staticprotected

Static array of ints to hold conversion from pressure node numbers to actual node numbers

Referenced by oomph::QTaylorHoodElement< DIM >::p_nst(), and oomph::RefineableQTaylorHoodElement< DIM >::pressure_node_pt().

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

Public Member Functions

Protected Member Functions

Static Protected Attributes

Private Member Functions

Static Private Attributes

Additional Inherited Members

Detailed Description

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

Constructor & Destructor Documentation

◆ QTaylorHoodElement()

Member Function Documentation

◆ build_fp_press_adv_diff_robin_bc_element()

◆ dpshape_and_dptest_eulerian_nst() [1/3]

◆ dpshape_and_dptest_eulerian_nst() [2/3]

◆ dpshape_and_dptest_eulerian_nst() [3/3]

◆ dshape_and_dtest_eulerian_at_knot_nst() [1/4]

◆ dshape_and_dtest_eulerian_at_knot_nst() [2/4]

◆ dshape_and_dtest_eulerian_at_knot_nst() [3/4]

◆ dshape_and_dtest_eulerian_at_knot_nst() [4/4]

◆ dshape_and_dtest_eulerian_nst()

◆ fix_pressure()

◆ get_dof_numbers_for_unknowns()

◆ identify_load_data()

◆ identify_pressure_data()

◆ Initial_Nvalue() [1/2]

◆ Initial_Nvalue() [2/2]

◆ is_pressure_node()

◆ ndof_types()

◆ npres_nst()

◆ output() [1/4]

◆ output() [2/4]

◆ output() [3/4]

◆ output() [4/4]

◆ p_local_eqn()

◆ p_nodal_index_nst()

◆ p_nst() [1/2]

◆ p_nst() [2/2]

◆ Pconv() [1/2]

◆ Pconv() [2/2]

◆ pshape_nst() [1/4]

◆ pshape_nst() [2/4]

◆ pshape_nst() [3/4]

◆ pshape_nst() [4/4]

◆ required_nvalue()

Member Data Documentation

◆ Initial_Nvalue

◆ Pconv

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