Rodin/Variational/H1/H1Element.hpp file

Template implementation for H1Element class.

This file contains the template member function implementations for H1Element, including:

  • Basis function evaluation using modal Dubiner basis
  • First-order derivative computation via chain rule
  • Vandermonde matrix inversion for nodal-to-modal conversion

The implementation uses:

  • Segments: Classical Lagrange interpolation with GLL nodes
  • Triangles: Dubiner modal basis with Fekete nodes
  • Quadrilaterals: Tensor product of 1D GLL Lagrange bases
  • Tetrahedra: 3D Dubiner modal basis with Fekete nodes
  • Wedges: Product of triangle Fekete basis and 1D GLL basis

Namespaces

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

Classes

template<size_t K>
struct Rodin::Variational::PyramidIndex
Indexing of the tensor-product modes on the reference pyramid.
struct Rodin::Variational::PyramidIndex::IJ
Pair of tensor-product indices of a pyramid mode.
template<size_t K>
class Rodin::Variational::BernsteinPyramid
Bernstein basis on the reference pyramid.
template<size_t K>
class Rodin::Variational::PyramidModal
Modal basis on the reference pyramid.
template<size_t K>
class Rodin::Variational::VandermondePyramid
Vandermonde matrix of the modal basis on the reference pyramid.