reimplement interpolate function with averaging
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:
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Clement type interpolation (using local L2 projection)
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Evaluation in super-convergent points, i.e. average over evaluations in the element barycenters
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Least-squares approximation
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Therefore, the interface of
interpolate()must be extended to support some kind ofstrategyflag.