Reference documentation for deal.II version 9.1.1
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Public Member Functions | Static Public Member Functions | Static Private Member Functions | Private Attributes | List of all members
PolynomialsRaviartThomas< dim > Class Template Reference

#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 Hdiv-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 Qk. Therefore, the polynomial order of each component must be one order higher in the corresponding direction, yielding the polynomial spaces (Qk+1,k, Qk,k+1) and (Qk+1,k,k, Qk,k+1,k, Qk,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 Qk contains.

Definition at line 37 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 64 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 138 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 147 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 156 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 172 of file polynomials_raviart_thomas.cc.

◆ create_polynomials()

template<int dim>
std::vector< std::vector< Polynomials::Polynomial< double > > > PolynomialsRaviartThomas< dim >::create_polynomials ( const unsigned int  k)
staticprivate

A static member function that creates the polynomial space we use to initialize the polynomial_space member variable.

Definition at line 47 of file polynomials_raviart_thomas.cc.

Member Data Documentation

◆ my_degree

template<int dim>
const unsigned int PolynomialsRaviartThomas< dim >::my_degree
private

The degree of this object as given to the constructor.

Definition at line 113 of file polynomials_raviart_thomas.h.

◆ polynomial_space

template<int dim>
const AnisotropicPolynomials<dim> PolynomialsRaviartThomas< dim >::polynomial_space
private

An object representing the polynomial space for a single component. We can re-use it by rotating the coordinates of the evaluation point.

Definition at line 119 of file polynomials_raviart_thomas.h.

◆ n_pols

template<int dim>
const unsigned int PolynomialsRaviartThomas< dim >::n_pols
private

Number of Raviart-Thomas polynomials.

Definition at line 124 of file polynomials_raviart_thomas.h.


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