Reference documentation for deal.II version 9.3.3

#include <deal.II/base/polynomials_raviart_thomas.h>
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 
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 
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 48 of file polynomials_raviart_thomas.h.
PolynomialsRaviartThomas< dim >::PolynomialsRaviartThomas  (  const unsigned int  k  ) 
Constructor. Creates all basis functions for RaviartThomas polynomials of given degree.
Definition at line 38 of file polynomials_raviart_thomas.cc.

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.

inlineoverridevirtual 
Return the name of the space, which is RaviartThomas
.
Implements TensorPolynomialsBase< dim >.
Definition at line 119 of file polynomials_raviart_thomas.h.

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.

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.

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.

inlineinherited 
Return the number of polynomials.
Definition at line 155 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 164 of file tensor_polynomials_base.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 106 of file polynomials_raviart_thomas.h.

privateinherited 
The highest polynomial degree of this functions represented by this object.
Definition at line 143 of file tensor_polynomials_base.h.

privateinherited 
The number of polynomials represented by this object.
Definition at line 148 of file tensor_polynomials_base.h.