Raviart-Thomas element of order 0. More...

#include <fe_rt.hh>

Inheritance diagram for FE_RT0< dim, spacedim >:

Collaboration diagram for FE_RT0< dim, spacedim >:

Public Member Functions
	FE_RT0 ()
	Constructor. More...

double	basis_value (const unsigned int i, const arma::vec::fixed< dim > &p) const
	The scalar variant of basis_vector must be implemented but may not be used. More...

arma::vec::fixed< dim >	basis_grad (const unsigned int i, const arma::vec::fixed< dim > &p) const
	The scalar variant of basis_grad_vector must be implemented but may not be used. More...

arma::vec::fixed< dim >	basis_vector (const unsigned int i, const arma::vec::fixed< dim > &p) const
	Returns the `ith` basis function evaluated at the point `p`. More...

arma::mat::fixed< dim, dim >	basis_grad_vector (const unsigned int i, const arma::vec::fixed< dim > &p) const
	Returns the gradient of the `ith` basis function at the point `p`. More...

void	compute_node_matrix ()
	Computes the conversion matrix from internal basis to shape functions. More...

FEInternalData *	initialize (const Quadrature< dim > &q, UpdateFlags flags)
	Calculates the data on the reference cell. More...

UpdateFlags	update_each (UpdateFlags flags)
	Decides which additional quantities have to be computed for each cell. More...

virtual void	fill_fe_values (const Quadrature< dim > &q, FEInternalData &data, FEValuesData< dim, spacedim > &fv_data)
	Computes the shape function values and gradients on the actual cell and fills the FEValues structure. More...

virtual	~FE_RT0 ()
	Destructor. More...

Public Member Functions inherited from FiniteElement< dim, spacedim >
	FiniteElement ()
	Constructor. More...

void	init ()
	Clears all internal structures. More...

const unsigned int	n_dofs () const
	Returns the number of degrees of freedom needed by the finite element. More...

const unsigned int	n_object_dofs (unsigned int object_dim, DofMultiplicity multiplicity)
	Returns the number of single dofs/dof pairs/triples/sextuples that lie on a single geometric entity of the dimension `object_dim`. More...

virtual const unsigned int	polynomial_order () const
	Returns the maximum degree of space of polynomials contained in the finite element space. More...

const bool	is_scalar () const
	Indicates whether the finite element function space is scalar or vectorial. More...

const std::vector< arma::vec::fixed< dim > > &	get_generalized_support_points ()
	Returns either the generalized support points (if they are defined) or the unit support points. More...

virtual	~FiniteElement ()
	Destructor. More...

Static Public Attributes
static const unsigned int	n_raw_functions = dim+1
	Number of raw basis functions. More...

Additional Inherited Members
Protected Attributes inherited from FiniteElement< dim, spacedim >
unsigned int	number_of_dofs
	Total number of degrees of freedom at one finite element. More...

unsigned int	number_of_single_dofs [dim+1]
	Number of single dofs at one geometrical entity of the given dimension (point, line, triangle, tetrahedron). More...

unsigned int	number_of_pairs [dim+1]
	Number of pairs of dofs at one geometrical entity of the given dimension (applicable to lines and triangles). More...

unsigned int	number_of_triples [dim+1]
	Number of triples of dofs associated to one triangle. More...

unsigned int	number_of_sextuples [dim+1]
	Number of sextuples of dofs associated to one triangle. More...

unsigned int	order
	Polynomial order - to be possibly used in hp methods. More...

bool	is_scalar_fe
	Indicator of scalar versus vectorial finite element. More...

arma::mat	node_matrix
	Matrix that determines the coefficients of the raw basis functions from the values at the support points. More...

std::vector< arma::vec::fixed< dim > >	unit_support_points
	Support points for Lagrangean finite elements. More...

std::vector< arma::vec::fixed< dim > >	generalized_support_points
	Support points for non-Lagrangean finite elements. More...

Detailed Description

template<unsigned int dim, unsigned int spacedim>
class FE_RT0< dim, spacedim >

Raviart-Thomas element of order 0.

The lowest order Raviart-Thomas finite element with linear basis functions and continuous normal components across element sides.

Definition at line 33 of file fe_rt.hh.

Constructor & Destructor Documentation

template<unsigned int dim, unsigned int spacedim>

FE_RT0< dim, spacedim >::FE_RT0 ( )

Constructor.

Definition at line 132 of file fe_rt.hh.

template<unsigned int dim, unsigned int spacedim>

virtual FE_RT0< dim, spacedim >::~FE_RT0 ( )

inlinevirtual

Destructor.

Definition at line 118 of file fe_rt.hh.

Member Function Documentation

template<unsigned int dim, unsigned int spacedim>

arma::vec::fixed< dim > FE_RT0< dim, spacedim >::basis_grad	(	const unsigned int	i,
		const arma::vec::fixed< dim > &	p
	)		const

virtual

The scalar variant of basis_grad_vector must be implemented but may not be used.

Implements FiniteElement< dim, spacedim >.

Definition at line 166 of file fe_rt.hh.

template<unsigned int dim, unsigned int spacedim>

arma::mat::fixed< dim, dim > FE_RT0< dim, spacedim >::basis_grad_vector	(	const unsigned int	i,
		const arma::vec::fixed< dim > &	p
	)		const

virtual

Returns the gradient of the ith basis function at the point p.

Parameters

i	Number of the basis function.
p	Point of evaluation.

Implements FiniteElement< dim, spacedim >.

Definition at line 186 of file fe_rt.hh.

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template<unsigned int dim, unsigned int spacedim>

double FE_RT0< dim, spacedim >::basis_value	(	const unsigned int	i,
		const arma::vec::fixed< dim > &	p
	)		const

virtual

The scalar variant of basis_vector must be implemented but may not be used.

Implements FiniteElement< dim, spacedim >.

Definition at line 158 of file fe_rt.hh.

template<unsigned int dim, unsigned int spacedim>

arma::vec::fixed< dim > FE_RT0< dim, spacedim >::basis_vector	(	const unsigned int	i,
		const arma::vec::fixed< dim > &	p
	)		const

virtual

Returns the ith basis function evaluated at the point p.

Parameters

i	Number of the basis function.
p	Point of evaluation.

Implements FiniteElement< dim, spacedim >.

Definition at line 173 of file fe_rt.hh.

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template<unsigned int dim, unsigned int spacedim>

void FE_RT0< dim, spacedim >::compute_node_matrix ( )

virtual

Computes the conversion matrix from internal basis to shape functions.

Initializes the node_matrix for computing the coefficients of the raw basis functions from values at support points. Since Raviart-Thomas element is not Lagrangean, the method has to be reimplemented.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 194 of file fe_rt.hh.

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template<unsigned int dim, unsigned int spacedim>

void FE_RT0< dim, spacedim >::fill_fe_values	(	const Quadrature< dim > &	q,
		FEInternalData &	data,
		FEValuesData< dim, spacedim > &	fv_data
	)

inlinevirtual

Computes the shape function values and gradients on the actual cell and fills the FEValues structure.

Parameters

q	Quadrature.
data	The precomputed finite element data on the reference cell.
fv_data	The data to be computed.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 298 of file fe_rt.hh.

template<unsigned int dim, unsigned int spacedim>

FEInternalData * FE_RT0< dim, spacedim >::initialize	(	const Quadrature< dim > &	q,
		UpdateFlags	flags
	)

virtual

Calculates the data on the reference cell.

Parameters

q	Quadrature.
flags	Flags that indicate what quantities should be calculated.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 232 of file fe_rt.hh.

template<unsigned int dim, unsigned int spacedim>

UpdateFlags FE_RT0< dim, spacedim >::update_each ( UpdateFlags flags )

inlinevirtual

Decides which additional quantities have to be computed for each cell.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 284 of file fe_rt.hh.

Member Data Documentation

template<unsigned int dim, unsigned int spacedim>

const unsigned int FE_RT0< dim, spacedim >::n_raw_functions = dim+1

static

Number of raw basis functions.

Definition at line 48 of file fe_rt.hh.

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

/opt/flow123d/flow123d/src/fem/fe_rt.hh

Public Member Functions

Static Public Attributes

Additional Inherited Members

Detailed Description

template<unsigned int dim, unsigned int spacedim> class FE_RT0< dim, spacedim >

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<unsigned int dim, unsigned int spacedim>
class FE_RT0< dim, spacedim >