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
Module for writing high level abstract expressions.
namespace Rodin::Variational
Module which provides the necessary tools for constructing and solving variational problems.

Classes

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.