/usr/include/deal.II/fe/fe_trace.h is in libdeal.ii-dev 8.5.1-3.
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//
// Copyright (C) 2000 - 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_trace_h
#define dealii__fe_trace_h
#include <deal.II/base/config.h>
#include <deal.II/base/tensor_product_polynomials.h>
#include <deal.II/fe/fe_poly_face.h>
#include <deal.II/fe/fe_q.h>
#include <deal.II/fe/fe_face.h>
DEAL_II_NAMESPACE_OPEN
/**
* A finite element, which is the trace of FE_Q elements, that is a tensor
* product of polynomials on the faces, undefined in the interior of the cells
* and continuous. The basis functions on the faces are formed by a tensor
* product of 1D Lagrange polynomials with equidistant points up to degree 2
* and Gauss-Lobatto points starting from degree 3.
*
* This finite element is the trace space of FE_Q on the faces.
*
* @note Since these are only finite elements on faces, only FEFaceValues and
* FESubfaceValues will be able to extract reasonable values from any face
* polynomial. In order to make the use of FESystem simpler, FEValues objects
* will not fail using this finite element space, but all shape function
* values extracted will equal to zero.
*/
template <int dim, int spacedim=dim>
class FE_TraceQ : public FE_PolyFace<TensorProductPolynomials<dim-1>, dim, spacedim>
{
public:
/**
* Constructor for tensor product polynomials of degree <tt>p</tt>. The
* shape functions created using this constructor correspond to Legendre
* polynomials in each coordinate direction.
*/
FE_TraceQ(unsigned int p);
/**
* @p clone function instead of a copy constructor.
*
* This function is needed by the constructors of @p FESystem.
*/
virtual FiniteElement<dim,spacedim> *clone() const;
/**
* Return a string that uniquely identifies a finite element. This class
* returns <tt>FE_DGQ<dim>(degree)</tt>, with <tt>dim</tt> and
* <tt>degree</tt> replaced by appropriate values.
*/
virtual std::string get_name () const;
/**
* This function returns @p true, if the shape function @p shape_index has
* non-zero function values somewhere on the face @p face_index.
*/
virtual bool has_support_on_face (const unsigned int shape_index,
const unsigned int face_index) const;
/**
* Return a list of constant modes of the element. For this element, it
* simply returns one row with all entries set to true.
*/
virtual std::pair<Table<2,bool>, std::vector<unsigned int> >
get_constant_modes () const;
/**
* Return whether this element implements its hanging node constraints in
* the new way, which has to be used to make elements "hp compatible".
*/
virtual bool hp_constraints_are_implemented () const;
/**
* Return the matrix interpolating from a face of of one element to the face
* of the neighboring element. The size of the matrix is then
* <tt>source.dofs_per_face</tt> times <tt>this->dofs_per_face</tt>. This
* element only provides interpolation matrices for elements of the same
* type and FE_Nothing. For all other elements, an exception of type
* FiniteElement<dim,spacedim>::ExcInterpolationNotImplemented is thrown.
*/
virtual void
get_face_interpolation_matrix (const FiniteElement<dim,spacedim> &source,
FullMatrix<double> &matrix) const;
/**
* Return the matrix interpolating from a face of of one element to the face
* of the neighboring element. The size of the matrix is then
* <tt>source.dofs_per_face</tt> times <tt>this->dofs_per_face</tt>. This
* element only provides interpolation matrices for elements of the same
* type and FE_Nothing. For all other elements, an exception of type
* FiniteElement<dim,spacedim>::ExcInterpolationNotImplemented is thrown.
*/
virtual void
get_subface_interpolation_matrix (const FiniteElement<dim,spacedim> &source,
const unsigned int subface,
FullMatrix<double> &matrix) const;
/**
* Return whether this element dominates the one given as argument when they
* meet at a common face, whether it is the other way around, whether
* neither dominates, or if either could dominate.
*
* For a definition of domination, see FiniteElementDomination::Domination
* and in particular the
* @ref hp_paper "hp paper".
*/
virtual
FiniteElementDomination::Domination
compare_for_face_domination (const FiniteElement<dim,spacedim> &fe_other) const;
private:
/**
* Store a copy of FE_Q for delegating the hp-constraints functionality.
*/
FE_Q<dim, spacedim> fe_q;
/**
* Return vector with dofs per vertex, line, quad, hex.
*/
static std::vector<unsigned int> get_dpo_vector (const unsigned int deg);
};
/**
* FE_TraceQ in 1D, i.e., with degrees of freedom on the element vertices.
*/
template <int spacedim>
class FE_TraceQ<1,spacedim> : public FE_FaceQ<1,spacedim>
{
public:
/**
* Constructor.
*/
FE_TraceQ (const unsigned int p);
/**
* Return the name of the element
*/
std::string get_name() const;
};
DEAL_II_NAMESPACE_CLOSE
#endif
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