Dune::ACFem::L2ProjectionOperator< DiscreteFunction, Functional > Class Template Reference

Compute the L2-projection of the given functional to a discrete space. More...

#include <dune/acfem/operators/l2projection.hh>

Detailed Description

template<class DiscreteFunction, class Functional>
class Dune::ACFem::L2ProjectionOperator< DiscreteFunction, Functional >

Compute the L2-projection of the given functional to a discrete space.

This is meant for continuous finite elements. Consequently, we have to do "hard" work here and assemble and invert the mass matrix by means of a CG method. Fortunately, the condition of the mass-matrix should be bounded independently of the mesh width after applying Jacobian preconditioning.

Parameters

Functional	The Domain type, has to satisfiy the DiscreteLinearFunctional interface.
DiscreteFunction	The Range type. Some Fem::DiscreteFunction.

See, e.g., L2InnerProductFunctional for an example of what may be passed as argument ot L2Projection::operator() in a more concrete setting. However, any DiscreteLinearFunctional realization should do. E.g. for the DiracDistribution this projection also successfully computes an L2-Riesz representation. Any linear functional will do, as a FEM space is of finite dimension. However, if the underlying non-discrete functional is discontinuous, then it is unlikely that there will be a uniform bound for the L2-norm of the representative which is independent from mesh refinement.

Note

We cannot obey the Fem::Operator interface as we map DiscreteLinearFunctional instances, not Fem::Function instances, to Fem::DiscreteFunction instances.

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The documentation for this class was generated from the following file:

• dune/acfem/operators/l2projection.hh