#include <deal.II/base/polynomials_raviart_thomas.h>

Inheritance diagram for PolynomialsRaviartThomas< dim >:

Public Member Functions
	PolynomialsRaviartThomas (const unsigned int k)

void	evaluate (const Point< dim > &unit_point, std::vector< Tensor< 1, dim >> &values, std::vector< Tensor< 2, dim >> &grads, std::vector< Tensor< 3, dim >> &grad_grads, std::vector< Tensor< 4, dim >> &third_derivatives, std::vector< Tensor< 5, dim >> &fourth_derivatives) const override

std::string	name () const override

virtual std::unique_ptr< TensorPolynomialsBase< dim > >	clone () const override

Public Member Functions inherited from TensorPolynomialsBase< dim >
	TensorPolynomialsBase (const unsigned int deg, const unsigned int n_polynomials)

	TensorPolynomialsBase (TensorPolynomialsBase< dim > &&)=default

	TensorPolynomialsBase (const TensorPolynomialsBase< dim > &)=default

virtual	~TensorPolynomialsBase ()=default

unsigned int	n () const

unsigned int	degree () const

Static Public Member Functions
static unsigned int	n_polynomials (const unsigned int degree)

Static Private Member Functions
static std::vector< std::vector< Polynomials::Polynomial< double > > >	create_polynomials (const unsigned int k)

Private Attributes
const AnisotropicPolynomials< dim >	polynomial_space

Detailed Description

template<int dim>
class PolynomialsRaviartThomas< dim >

This class implements the H^div-conforming, vector-valued Raviart-Thomas polynomials as described in the book by Brezzi and Fortin.

The Raviart-Thomas polynomials are constructed such that the divergence is in the tensor product polynomial space Q_k. Therefore, the polynomial order of each component must be one order higher in the corresponding direction, yielding the polynomial spaces (Q_k+1,k, Q_k,k+1) and (Q_k+1,k,k, Q_k,k+1,k, Q_k,k,k+1) in 2D and 3D, resp.

Author: Guido Kanschat

Date: 2005

Definition at line 50 of file polynomials_raviart_thomas.h.

Constructor & Destructor Documentation

◆ PolynomialsRaviartThomas()

template<int dim>

PolynomialsRaviartThomas< dim >::PolynomialsRaviartThomas ( const unsigned int k )

Constructor. Creates all basis functions for Raviart-Thomas polynomials of given degree.

k: the degree of the Raviart-Thomas-space, which is the degree of the largest tensor product polynomial space Q_k contains.

Definition at line 38 of file polynomials_raviart_thomas.cc.

Member Function Documentation

◆ evaluate()

template<int dim>

void PolynomialsRaviartThomas< dim >::evaluate	(	const Point< dim > &	unit_point,
		std::vector< Tensor< 1, dim >> &	values,
		std::vector< Tensor< 2, dim >> &	grads,
		std::vector< Tensor< 3, dim >> &	grad_grads,
		std::vector< Tensor< 4, dim >> &	third_derivatives,
		std::vector< Tensor< 5, dim >> &	fourth_derivatives
	)		const

overridevirtual

Compute the value and the first and second derivatives of each Raviart- Thomas polynomial at unit_point.

The size of the vectors must either be zero or equal n(). In the first case, the function will not compute these values.

If you need values or derivatives of all tensor product polynomials then use this function, rather than using any of the compute_value, compute_grad or compute_grad_grad functions, see below, in a loop over all tensor product polynomials.

Implements TensorPolynomialsBase< dim >.

Definition at line 64 of file polynomials_raviart_thomas.cc.

◆ name()

template<int dim>

std::string PolynomialsRaviartThomas< dim >::name

inlineoverridevirtual

Return the name of the space, which is RaviartThomas.

Implements TensorPolynomialsBase< dim >.

Definition at line 121 of file polynomials_raviart_thomas.h.

◆ n_polynomials()

template<int dim>

unsigned int PolynomialsRaviartThomas< dim >::n_polynomials ( const unsigned int degree )

static

Return the number of polynomials in the space RT(degree) without requiring to build an object of PolynomialsRaviartThomas. This is required by the FiniteElement classes.

Definition at line 173 of file polynomials_raviart_thomas.cc.

◆ clone()

template<int dim>

std::unique_ptr< TensorPolynomialsBase< dim > > PolynomialsRaviartThomas< dim >::clone

overridevirtual

A sort of virtual copy constructor, this function returns a copy of the polynomial space object. Derived classes need to override the function here in this base class and return an object of the same type as the derived class.

Some places in the library, for example the constructors of FE_PolyTensor, need to make copies of polynomial spaces without knowing their exact type. They do so through this function.

Implements TensorPolynomialsBase< dim >.

Definition at line 189 of file polynomials_raviart_thomas.cc.