template<class Derived>
Rodin::Variational::FiniteElementSpaceMappingBase class

Base class for mappings taking functions defined on mesh elements to reference elements.

For all $ \tau \in \mathcal{T}_h $ the mapping

\[ \psi : V(\tau) \rightarrow V(K) \]

takes functions defined on the physical Banach space $ V(\tau) $ to the reference Banach space $ V(K) $ . Here $ \tau = x(K) $ is the physical element, $ K $ is the reference element, and $ x : K \rightarrow \tau $ is the polytope transformation.

Public functions

auto operator()(const Math::SpatialVector<Real>& r) const -> auto
Evaluates the mapped function on the reference coordinates.

Function documentation

template<class Derived>
auto Rodin::Variational::FiniteElementSpaceMappingBase<Derived>::operator()(const Math::SpatialVector<Real>& r) const

Evaluates the mapped function on the reference coordinates.

For the given function $ v \in V(\tau) $ , performs the following evaluation:

\[ \psi(v)(r) \]

on the reference coordinates $ r \in K $ .