raviartthomassimplexbasis.hh

// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
// vi: set et ts=4 sw=2 sts=2:
#ifndef DUNE_RAVIARTTHOMASBASIS_HH
#define DUNE_RAVIARTTHOMASBASIS_HH
 
#include <fstream>
#include <dune/common/exceptions.hh>
 
#include <dune/localfunctions/utility/defaultbasisfactory.hh>
#include "raviartthomassimplexinterpolation.hh"
#include "raviartthomassimplexprebasis.hh"
 
namespace Dune
{
 /*
  * `RTPreBasisFactory` provides a basis for the Raviart-Thomas function space.
  * `RaviartThomasL2InterpolationFactory` provides the linear functionals.
  *
  * `Defaultbasisfactory::create` first builds the function space and the linear functionals.
  * Then the constructor of `BasisMatrix` gets called. There the matrix
  *
  * \begin{equation}
  *   A_{i,j} := N_j(\phi_i)
  * \end{equation}
  *
  * with linear functionals $N_j$ and basisfunctions $\phi_i$ gets assembled.
  * Then the matrix gets inverted and is then used as a coefficent matrix for the standard monomial basis.
  *
  * For more details on the theory see the first chapter "Construction of Local Finite Element Spaces Using the Generic Reference Elements"
  * of the book "Advances in Dune" by Dedner, Flemisch and Klöfkorn published in 2012.
  */
 
  template< unsigned int dim, class SF, class CF >
  struct RaviartThomasBasisFactory
    : public DefaultBasisFactory< RTPreBasisFactory<dim,CF>,
          RaviartThomasL2InterpolationFactory<dim,CF>,
          dim,dim,SF,CF >
  {};
}
 
#endif // #ifndef DUNE_RAVIARTTHOMASBASIS_HH