reimplement interpolate function with averaging
Replace Dune::Functions::interpolate
with own implementation based on the dunefunctions implementation. Here, I want to allow nonsmooth (noncontinuouse) functions in the interpolation. Thus simple nodalinterpolation does not work. A first strategy is implementated, namely nodeaveraging. 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 superconvergent points, i.e. average over evaluations in the element barycenters

Leastsquares approximation

Therefore, the interface of
interpolate()
must be extended to support some kind ofstrategy
flag.