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.