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

Public Member Functions
	PolynomialsRaviartThomas (const unsigned int k)

void	compute (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

unsigned int	n () const

unsigned int	degree () const

std::string	name () const

Static Public Member Functions
static unsigned int	compute_n_pols (unsigned int degree)

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

Private Attributes
const unsigned int	my_degree

const AnisotropicPolynomials< dim >	polynomial_space

const unsigned int	n_pols

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 49 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 31 of file polynomials_raviart_thomas.cc.

Member Function Documentation

◆ compute()

template<int dim>

void PolynomialsRaviartThomas< dim >::compute	(	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

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.

Definition at line 59 of file polynomials_raviart_thomas.cc.

◆ n()

template<int dim>

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

inline

Return the number of Raviart-Thomas polynomials.

Definition at line 134 of file polynomials_raviart_thomas.h.

◆ degree()

template<int dim>

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

inline

Return the degree of the Raviart-Thomas space, which is one less than the highest polynomial degree.

Definition at line 143 of file polynomials_raviart_thomas.h.

◆ name()

template<int dim>

std::string PolynomialsRaviartThomas< dim >::name ( ) const

inline

Return the name of the space, which is RaviartThomas.

Definition at line 152 of file polynomials_raviart_thomas.h.

◆ compute_n_pols()

template<int dim>

unsigned int PolynomialsRaviartThomas< dim >::compute_n_pols ( 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 158 of file polynomials_raviart_thomas.cc.