H1Element.h file

Defines the H1Element class for H1-conforming Lagrange finite elements.

This file provides the implementation of high-order H1-conforming Lagrange finite elements. These elements are characterized by:

Continuous basis functions (H¹-conforming)
Lagrange nodal property:
Arbitrary polynomial degree K
Support for scalar and vector-valued fields

Namespaces

namespace Rodin: The Rodin library for finite element methods and shape optimization.
namespace Rodin::FormLanguage: Namespace Rodin::FormLanguage.
namespace Rodin::Variational: Namespace Rodin::Variational.

Classes

template<size_t K, class Range> struct Rodin::FormLanguage::Traits<Variational::H1Element<K, Range>>: Type traits for H1Element: exposes the scalar type and the range type of the element.
template<size_t K, class Scalar> class Rodin::Variational::H1Element: Degree k H1-conforming Lagrange element.
struct Rodin::Variational::H1Element::Tabulation: Basis values and derivatives tabulated on the reference element.
class Rodin::Variational::H1Element::LinearForm: Evaluates linear form at a given function/vector field.
class Rodin::Variational::H1Element::BasisFunction: Represents a Lagrange basis function of degree K.
template<size_t Order> class Rodin::Variational::H1Element::BasisFunction::DerivativeFunction: Represents a partial derivative of a basis function.
class Rodin::Variational::H1Element::BasisFunction::GradientFunction: Represents the gradient of a basis function.
template<size_t K, class Scalar> class Rodin::Variational::H1Element<K, Math::SpatialVector<Scalar>>: Continuous H1-conforming piecewise polynomial (degree k) vector Lagrange element.
class Rodin::Variational::H1Element<K, Math::SpatialVector<Scalar>>::LinearForm: Degree-of-freedom functional of the vector-valued H1 element.
class Rodin::Variational::H1Element<K, Math::SpatialVector<Scalar>>::BasisFunction: Basis function of the vector-valued H1 element.
template<size_t Order> class Rodin::Variational::H1Element<K, Math::SpatialVector<Scalar>>::BasisFunction::DerivativeFunction: Represents a derivative function of a Pk vector element.
class Rodin::Variational::H1Element<K, Math::SpatialVector<Scalar>>::BasisFunction::JacobianFunction: Jacobian of a vector-valued H1 basis function.