Reference documentation for deal.II version GIT c00406db16 20230928 18:00:02+00:00

#include <deal.II/base/polynomials_raviart_thomas.h>
Public Member Functions  
PolynomialsRaviartThomas (const unsigned int degree_normal, const unsigned int degree_tangential)  
PolynomialsRaviartThomas (const unsigned int k)  
PolynomialsRaviartThomas (const PolynomialsRaviartThomas &other)=default  
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 
std::vector< Point< dim > >  get_polynomial_support_points () const 
unsigned int  n () const 
unsigned int  degree () const 
Static Public Member Functions  
static unsigned int  n_polynomials (const unsigned int normal_degree, const unsigned int tangential_degree) 
static unsigned int  n_polynomials (const unsigned int degree) 
static std::vector< unsigned int >  get_lexicographic_numbering (const unsigned int normal_degree, const unsigned int tangential_degree) 
Private Attributes  
const unsigned int  normal_degree 
const unsigned int  tangential_degree 
const AnisotropicPolynomials< dim >  polynomial_space 
std::vector< unsigned int >  lexicographic_to_hierarchic 
std::vector< unsigned int >  hierarchic_to_lexicographic 
std::array< std::vector< unsigned int >, dim >  renumber_aniso 
const unsigned int  polynomial_degree 
const unsigned int  n_pols 
This class implements the H^{div}conforming, vectorvalued RaviartThomas polynomials as described in the book by Brezzi and Fortin.
The RaviartThomas 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.
Definition at line 50 of file polynomials_raviart_thomas.h.
PolynomialsRaviartThomas< dim >::PolynomialsRaviartThomas  (  const unsigned int  degree_normal, 
const unsigned int  degree_tangential  
) 
Constructor. Creates all basis functions for RaviartThomas polynomials of given degree in normal and tangential directions. The usual FE_RaviartThomas and FE_RaviartThomasNodal classes will use degree + 1
and degree
in the two directions, respectively.
Definition at line 64 of file polynomials_raviart_thomas.cc.
PolynomialsRaviartThomas< dim >::PolynomialsRaviartThomas  (  const unsigned int  k  ) 
Constructor, using the common RaviartThomas space of degree k + 1
in normal direction and k
in the tangential directions.
Definition at line 126 of file polynomials_raviart_thomas.cc.

default 
Copy constructor.

overridevirtual 
Compute the value and derivatives of each RaviartThomas 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.
Implements TensorPolynomialsBase< dim >.
Definition at line 134 of file polynomials_raviart_thomas.cc.

overridevirtual 
Return the name of the space, which is PolynomialsRaviartThomas
.
Implements TensorPolynomialsBase< dim >.
Definition at line 227 of file polynomials_raviart_thomas.cc.

static 
Return the number of polynomials in the space without requiring to build an object of PolynomialsRaviartThomas. This is required by the FiniteElement classes.
Definition at line 245 of file polynomials_raviart_thomas.cc.

static 
Variant of the n_polynomials() function taking only a single argument degree
, assuming degree + 1
in the normal direction and degree
in the tangential directions.
Definition at line 236 of file polynomials_raviart_thomas.cc.

static 
Compute the lexicographic to hierarchic numbering underlying this class, computed as a free function.
Definition at line 257 of file polynomials_raviart_thomas.cc.

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 322 of file polynomials_raviart_thomas.cc.
std::vector< Point< dim > > PolynomialsRaviartThomas< dim >::get_polynomial_support_points 
Compute the generalized support points in the ordering used by the polynomial shape functions. Note that these points are not support points in the classical sense as the Lagrange polynomials of the different components have different points, which need to be combined in terms of Piola transforms.
Definition at line 331 of file polynomials_raviart_thomas.cc.

inlineinherited 
Return the number of polynomials.
Definition at line 152 of file tensor_polynomials_base.h.

inlineinherited 
Return the highest polynomial degree of polynomials represented by this class. A derived class may override this if its value is different from my_degree
.
Definition at line 161 of file tensor_polynomials_base.h.

private 
The given degree in the normal direction.
Definition at line 143 of file polynomials_raviart_thomas.h.

private 
The given degree in the tangential direction.
Definition at line 148 of file polynomials_raviart_thomas.h.

private 
An object representing the polynomial space for a single component. We can reuse it by rotating the coordinates of the evaluation point.
Definition at line 154 of file polynomials_raviart_thomas.h.

private 
Renumbering from lexicographic to hierarchic order.
Definition at line 159 of file polynomials_raviart_thomas.h.

private 
Renumbering from hierarchic to lexicographic order. Inverse of lexicographic_to_hierarchic.
Definition at line 165 of file polynomials_raviart_thomas.h.

private 
Renumbering from shifted polynomial spaces to lexicographic one.
Definition at line 170 of file polynomials_raviart_thomas.h.

privateinherited 
The highest polynomial degree of this functions represented by this object.
Definition at line 140 of file tensor_polynomials_base.h.

privateinherited 
The number of polynomials represented by this object.
Definition at line 145 of file tensor_polynomials_base.h.