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cubichermitebasis.hh File Reference

This file provides an implementation of the cubic Hermite finite element in 1 to 3 dimensions. More...

`#include <algorithm>`
`#include <array>`
`#include <numeric>`
`#include <type_traits>`
`#include <vector>`
`#include <dune/common/exceptions.hh>`
`#include <dune/common/fmatrix.hh>`
`#include <dune/common/fvector.hh>`
`#include <dune/common/rangeutilities.hh>`
`#include <dune/grid/common/mcmgmapper.hh>`
`#include <dune/localfunctions/common/localbasis.hh>`
`#include <dune/localfunctions/common/localfiniteelementtraits.hh>`
`#include <dune/localfunctions/common/localkey.hh>`
`#include <dune/functions/common/mapperutilities.hh>`
`#include <dune/functions/common/squeezetensor.hh>`
`#include <dune/functions/functionspacebases/defaultglobalbasis.hh>`
`#include <dune/functions/functionspacebases/functionaldescriptor.hh>`
`#include <dune/functions/functionspacebases/leafprebasismappermixin.hh>`
`#include <dune/functions/functionspacebases/nodes.hh>`
`#include <dune/functions/functionspacebases/transformedfiniteelementmixin.hh>`
`#include <dune/functions/analyticfunctions/monomialset.hh>`

Go to the source code of this file.

## Classes

struct | Dune::Functions::H2LocalBasisTraits< DF, n, D, RF, m, R, J, H >
class | Dune::Functions::CubicHermiteNode< GV, R, reduced >
class | Dune::Functions::CubicHermitePreBasis< GV, R, reduced >
| A pre-basis for a Hermitebasis. More...

## Namespaces

namespace | Dune
namespace | Dune::Functions
namespace | Dune::Functions::BasisFactory

## Typedefs

template<class GV, bool reduced = false, class R = double>
using | Dune::Functions::CubicHermiteBasis = DefaultGlobalBasis<CubicHermitePreBasis<GV, R, reduced> >
| Nodal basis of a scalar cubic Hermite finite element space.

## Detailed Description

This file provides an implementation of the cubic Hermite finite element in 1 to 3 dimensions.

For reference, see[Ciarlet, The Finite Element Method for Elliptic Problems, 2002]. It contains in the following order:

- A GlobalBasis typedef CubicHermiteBasis
- A template H2LocalBasisTraits, extending the dune-localfunctions LocalBasisTraits by an exported Hessiantype
- A template CubicHermiteLocalFiniteElement providing an implementation of the LocalFiniteElement interface, along with its subparts (Impl namespace)
- A template CubicHermiteNode
- A template CubicHermitePreBasis
- Two factories hermite() and reducedHermite() in the BasisFactory namespace