Grad.h file

Gradient operator specialization for H1 (higher-order Lagrange) functions.

For H1<K> functions, the gradient is polynomial of degree K-1 on each element:

where are the H1<K> basis functions.

Namespaces

namespace Rodin: The Rodin library for finite element methods and shape optimization.
namespace Rodin::Variational: Finite element spaces, fields, and variational problems.
namespace Rodin::FormLanguage: Typed expressions for constructing variational forms.

Classes

template<size_t K, class Scalar, class Mesh, class Data> class Rodin::Variational::Grad<GridFunction<H1<K, Scalar, Mesh>, Data>>: Gradient of a GridFunction on H1<K> space.
template<size_t K, class NestedDerived, class Scalar, class Mesh, ShapeFunctionSpaceType SpaceType> class Rodin::Variational::Grad<ShapeFunction<NestedDerived, H1<K, Scalar, Mesh>, SpaceType>>: Gradient of a ShapeFunction on H1<K> space.
struct Rodin::Variational::Grad<ShapeFunction<NestedDerived, H1<K, Scalar, Mesh>, SpaceType>>::Cache: Physical gradients prepared by the current integration-point bind.
template<size_t K, class Scalar, class Mesh, class Data> struct Rodin::FormLanguage::Traits<Variational::Grad<Variational::GridFunction<Variational::H1<K, Math::SpatialMatrix<Scalar>, Mesh>, Data>>>: Rank-three physical gradient range for the matrix H1 solution.
template<size_t K, class Scalar, class Mesh, class Derived, Variational::ShapeFunctionSpaceType Space> struct Rodin::FormLanguage::Traits<Variational::Grad<Variational::ShapeFunction<Derived, Variational::H1<K, Math::SpatialMatrix<Scalar>, Mesh>, Space>>>: Rank-three physical gradient range for matrix H1 shape functions.
template<size_t K, class Scalar, class Mesh, class Data> class Rodin::Variational::Grad<GridFunction<H1<K, Math::SpatialMatrix<Scalar>, Mesh>, Data>>: Physical gradient of a matrix H1 solution, with derivative axis last. Uses this family's scalar basis and component ordering.
template<size_t K, class Scalar, class Mesh, class Derived, ShapeFunctionSpaceType Space> class Rodin::Variational::Grad<ShapeFunction<Derived, H1<K, Math::SpatialMatrix<Scalar>, Mesh>, Space>>: Physical gradients of matrix H1 trial or test bases.