Towards robust h-multigrid for high-order mappings

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PR #614 introduces an application test case where a high-order mapping leads to invalid grid/mappings on coarser multigrid h-levels.

Generally speaking, there is no guarantee that h-multigrid is robust in combination with high-order mappings. Boundary layer mappings as described in PR #614 inherently lead to problems and can be seen as a practically relevant example. One could argue to use a linear mapping on the fine grid to solve the problem, but think of flow around curved bodies (in the most simple case a sphere or cylinder) where one wants to approximate the geometry at least by a quadratic mapping and - at the same time - use a grid stretching in walll-normal direction to resolve boundary layers.

Note that the same problem can occur when describing the fine level mapping by MappingQCache (e.g. some complex geometry in biomedical engineering) and when constructing the mappings on coarser grids by standard multigrid transfer operations.

I suggest to introduce in ExaDG the flexibility to choose the degree of the mappings on coarser multigrid levels independently of the degree of the fine level mapping. Regarding the parameters, there occur different questions:

• On the fine multigrid level, should we generally use the same mapping degree as used for the actual "PDE operator"? I would say "yes". We can safely assume that the fine level mapping prescribed by an application has to be valid. Otherwise we could not solve on that geometry/grid at all.
• On the coarser levels, is one single parameter (unsigned int mapping_degree_coarse_grids) for all the coarse grids enough, or do we even want to have more flexibility? I would say one parameter for all the coarse levels is enough. I could imagine that going to a linear mapping on coarser grids recovers robustness for many problems.

Of course, another and very general question concerns the implications of such a "variational crime" on multigrid convergence rates.