Public Member Functions | Static Public Member Functions | Static Private Member Functions | Private Attributes

PolynomialsRaviartThomas< dim > Class Template Reference
[Polynomials and polynomial spaces]

List of all members.

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) 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 47 of file polynomials_raviart_thomas.h.


Constructor & Destructor Documentation

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 contained.

Member Function Documentation

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 
) const

Computes 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.

template<int dim>
unsigned int PolynomialsRaviartThomas< dim >::n (  ) const [inline]

Returns the number of Raviart-Thomas polynomials.

Definition at line 159 of file polynomials_raviart_thomas.h.

References PolynomialsRaviartThomas< dim >::n_pols.

template<int dim>
unsigned int PolynomialsRaviartThomas< dim >::degree (  ) const [inline]

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

Definition at line 168 of file polynomials_raviart_thomas.h.

References PolynomialsRaviartThomas< dim >::my_degree.

template<int dim>
std::string PolynomialsRaviartThomas< dim >::name (  ) const [inline]

Return the name of the space , which is RaviartThomas.

Definition at line 177 of file polynomials_raviart_thomas.h.

template<int dim>
static 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.

template<int dim>
static std::vector<std::vector< Polynomials::Polynomial< double > > > PolynomialsRaviartThomas< dim >::create_polynomials ( const unsigned int  k ) [static, private]

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


Member Data Documentation

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

The degree of this object as given to the constructor.

Definition at line 126 of file polynomials_raviart_thomas.h.

Referenced by PolynomialsRaviartThomas< dim >::degree().

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 135 of file polynomials_raviart_thomas.h.

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

Number of Raviart-Thomas polynomials.

Definition at line 141 of file polynomials_raviart_thomas.h.

Referenced by PolynomialsRaviartThomas< dim >::n().


The documentation for this class was generated from the following file:
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deal.II documentation generated on Fri Feb 3 2012 06:04:10 by doxygen 1.7.2