Rodin/Variational/H1/Derivative.h file

Partial derivative operator specialization for H1 functions.

This file provides specialized implementations of the partial derivative operator for H1 GridFunctions. For an H1<K> function $ u $ , the partial derivative with respect to coordinate $ x_i $ is:

\[ \frac{\partial u}{\partial x_i} = (\nabla u) \cdot \mathbf{e}_i \]

For H1<K> elements, partial derivatives are polynomial of degree K-1 on each element.

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 Scalar, class Mesh, class Data>
struct Rodin::FormLanguage::Traits<Variational::Derivative<Variational::GridFunction<Variational::H1<K, Scalar, Mesh>, Data>>>
Type traits for Derivative over a grid function: exposes the finite element space, the operand type and the range type.
template<size_t K, class Scalar, class Mesh, class Data>
class Rodin::Variational::Derivative<GridFunction<H1<K, Scalar, Mesh>, Data>>
Derivative of an H1<K> GridFunction.