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//
// Copyright (C) 2003 - 2016 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------
#ifndef dealii__fe_bdm_h
#define dealii__fe_bdm_h
#include <deal.II/base/config.h>
#include <deal.II/base/table.h>
#include <deal.II/base/polynomials_bdm.h>
#include <deal.II/base/polynomial.h>
#include <deal.II/base/tensor_product_polynomials.h>
#include <deal.II/base/geometry_info.h>
#include <deal.II/fe/fe.h>
#include <deal.II/fe/fe_poly_tensor.h>
#include <vector>
DEAL_II_NAMESPACE_OPEN
/**
* The Brezzi-Douglas-Marini element.
*
* <h3>Degrees of freedom</h3>
*
* @todo The 3D version exhibits some numerical instabilities, in particular
* for higher order
*
* @todo Restriction matrices are missing.
*
* The matching pressure space for FE_BDM of order <i>k</i> is the element
* FE_DGP of order <i>k-1</i>.
*
* The BDM element of order @p p has <i>p+1</i> degrees of freedom on each
* face. These are implemented as the function values in the <i>p+1</i> Gauss
* points on each face.
*
* Additionally, for order greater or equal 2, we have additional
* <i>p(p-1)</i>, the number of vector valued polynomials in
* <i>P<sub>p</sub></i>, interior degrees of freedom. These are the vector
* function values in the first <i>p(p-1)/2</i> of the <i>p<sup>2</sup></i>
* Gauss points in the cell.
*/
template <int dim>
class FE_BDM
:
public FE_PolyTensor<PolynomialsBDM<dim>, dim>
{
public:
/**
* Constructor for the BDM element of degree @p p.
*/
FE_BDM (const unsigned int p);
/**
* Return a string that uniquely identifies a finite element. This class
* returns <tt>FE_BDM<dim>(degree)</tt>, with @p dim and @p degree replaced
* by appropriate values.
*/
virtual std::string get_name () const;
virtual FiniteElement<dim> *clone () const;
virtual void interpolate(std::vector<double> &local_dofs,
const std::vector<double> &values) const;
virtual void interpolate(std::vector<double> &local_dofs,
const std::vector<Vector<double> > &values,
unsigned int offset = 0) const;
virtual void interpolate(
std::vector<double> &local_dofs,
const VectorSlice<const std::vector<std::vector<double> > > &values) const;
private:
/**
* Only for internal use. Its full name is @p get_dofs_per_object_vector
* function and it creates the @p dofs_per_object vector that is needed
* within the constructor to be passed to the constructor of @p
* FiniteElementData.
*/
static std::vector<unsigned int>
get_dpo_vector (const unsigned int degree);
/**
* Compute the vector used for the @p restriction_is_additive field passed
* to the base class's constructor.
*/
static std::vector<bool>
get_ria_vector (const unsigned int degree);
/**
* Initialize the FiniteElement<dim>::generalized_support_points and
* FiniteElement<dim>::generalized_face_support_points fields. Called from
* the constructor. See the
* @ref GlossGeneralizedSupport "glossary entry on generalized support points"
* for more information.
*/
void initialize_support_points (const unsigned int bdm_degree);
/**
* The values in the face support points of the polynomials needed as test
* functions. The outer vector is indexed by quadrature points, the inner by
* the test function. The test function space is PolynomialsP<dim-1>.
*/
std::vector<std::vector<double> > test_values_face;
/**
* The values in the interior support points of the polynomials needed as
* test functions. The outer vector is indexed by quadrature points, the
* inner by the test function. The test function space is PolynomialsP<dim>.
*/
std::vector<std::vector<double> > test_values_cell;
};
DEAL_II_NAMESPACE_CLOSE
#endif
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