fe_hermite.h

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// -----------------------------------------------------------------------------
//
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception OR LGPL-2.1-or-later
// Copyright (C) 2023 - 2025 by the deal.II authors
//
// This file is part of the deal.II library.
//
// Detailed license information governing the source code and contributions
// can be found in LICENSE.md and CONTRIBUTING.md at the top level directory.
//
// -----------------------------------------------------------------------------
 
#ifndef dealii_fe_hermite_h
#define dealii_fe_hermite_h
 
#include <deal.II/base/config.h>
 
#include <deal.II/base/polynomials_hermite.h>
 
#include <deal.II/fe/fe_poly.h>
 
#include <string>
#include <vector>
 
DEAL_II_NAMESPACE_OPEN

 
 

template <int dim, int spacedim = dim>
class FE_Hermite : public FE_Poly<dim, spacedim>
{
public:
  FE_Hermite(const unsigned int fe_degree);
 
  // Other functions
  virtual std::string
  get_name() const override;

  virtual std::unique_ptr<FiniteElement<dim, spacedim>>
  clone() const override;

  virtual UpdateFlags
  requires_update_flags(const UpdateFlags update_flags) const override;

  virtual std::vector<std::pair<unsigned int, unsigned int>>
  hp_vertex_dof_identities(
    const FiniteElement<dim, spacedim> &fe_other) const override;

  virtual std::vector<std::pair<unsigned int, unsigned int>>
  hp_line_dof_identities(
    const FiniteElement<dim, spacedim> &fe_other) const override;

  virtual std::vector<std::pair<unsigned int, unsigned int>>
  hp_quad_dof_identities(const FiniteElement<dim, spacedim> &fe_other,
                         const unsigned int face_no = 0) const override;

  virtual FiniteElementDomination::Domination
  compare_for_domination(const FiniteElement<dim, spacedim> &other_fe,
                         const unsigned int codim) const override;

  std::vector<unsigned int>
  get_lexicographic_to_hierarchic_numbering() const;

  Table<2, unsigned int>
  get_dofs_corresponding_to_outward_normal_derivatives(
    const unsigned int derivative_order) const;

  virtual void
  fill_fe_values(
    const typename Triangulation<dim, spacedim>::cell_iterator &cell,
    const CellSimilarity::Similarity                            cell_similarity,
    const Quadrature<dim>                                      &quadrature,
    const Mapping<dim, spacedim>                               &mapping,
    const typename Mapping<dim, spacedim>::InternalDataBase &mapping_internal,
    const ::internal::FEValuesImplementation::MappingRelatedData<dim,
                                                                       spacedim>
                                                                  &mapping_data,
    const typename FiniteElement<dim, spacedim>::InternalDataBase &fe_internal,
    ::internal::FEValuesImplementation::FiniteElementRelatedData<dim,
                                                                       spacedim>
      &output_data) const override;
 
  using FiniteElement<dim, spacedim>::fill_fe_face_values;

  virtual void
  fill_fe_face_values(
    const typename Triangulation<dim, spacedim>::cell_iterator &cell,
    const unsigned int                                          face_no,
    const hp::QCollection<dim - 1>                             &quadrature,
    const Mapping<dim, spacedim>                               &mapping,
    const typename Mapping<dim, spacedim>::InternalDataBase &mapping_internal,
    const ::internal::FEValuesImplementation::MappingRelatedData<dim,
                                                                       spacedim>
                                                                  &mapping_data,
    const typename FiniteElement<dim, spacedim>::InternalDataBase &fe_internal,
    ::internal::FEValuesImplementation::FiniteElementRelatedData<dim,
                                                                       spacedim>
      &output_data) const override;
 
 
 
protected:
  virtual std::unique_ptr<
    typename FiniteElement<dim, spacedim>::InternalDataBase>
  get_data(
    const UpdateFlags             update_flags,
    const Mapping<dim, spacedim> &mapping,
    const Quadrature<dim>        &quadrature,
    ::internal::FEValuesImplementation::FiniteElementRelatedData<dim,
                                                                       spacedim>
      &output_data) const override
  {
    std::unique_ptr<typename FiniteElement<dim, spacedim>::InternalDataBase>
          data_ptr = FE_Poly<dim, spacedim>::get_data(update_flags,
                                                  mapping,
                                                  quadrature,
                                                  output_data);
    auto &data =
      dynamic_cast<typename FE_Poly<dim, spacedim>::InternalData &>(*data_ptr);
 
    const unsigned int n_q_points = quadrature.size();
 
    if ((update_flags & update_values) &&
        ((output_data.shape_values.n_rows() > 0) &&
         (output_data.shape_values.n_cols() == n_q_points)))
      data.shape_values = output_data.shape_values;
 
    return data_ptr;
  }
 
private:
  unsigned int regularity;
 
public:
  inline unsigned int
  get_regularity() const
  {
    return this->regularity;
  };
};

 
 
 
DEAL_II_NAMESPACE_CLOSE
 
#endif