Replace Dune::Functions::interpolate with own implementation based on the dune-functions implementation. Here, I want to allow non-smooth (non-continuouse) functions in the interpolation. Thus simple nodal-interpolation does not work. A first strategy is implementated, namely node-averaging. A counter is added that counts how often a values is added to a DOF and after the interpolation the DOF value is divided by this counter value.
Other strategies that could be added:
Clement type interpolation (using local L2 projection)
Evaluation in super-convergent points, i.e. average over evaluations in the element barycenters
Least-squares approximation
Therefore, the interface of interpolate() must be extended to support some kind of strategy flag.
Praetorius, Simon authored