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reimplement interpolate function with averaging

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Merged Praetorius, Simon requested to merge feature/interpolate into master Mar 26, 2019
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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.

Edited Apr 26, 2019 by Praetorius, Simon
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Source branch: feature/interpolate