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[WIP] HDiv bases (Raviart-Thomas and Brezzi-Douglas-Marini) on cubes and simplices

Jakub Both requested to merge feature/hdiv-bases into master

HDiv finite element bases (Raviart-Thomas and a Brezzi-Douglas-Marini) are added in the fashion of PQkNodaBasis. Additionally a test case is provided (Poisson equation discretized by RT(k) x P(k) and BDM(k+1) x P(k) elements in 2 and 3 dimensions).

Based on the Poisson test case:

  • Working: 2D: RT0 x P0, RT1 x P1, BDM1 x P0, BDM2 x P1 -- 3D: RT0 x P0, RT1 x P1.
  • Not working: 2D: RT2 x P2 (solver does not converge) -- 3D: BDM1 x P0 (no interpolation provided by dune-localfunctions).

Major issue:

  • Currently, interpolation does not work properly for HDiv elements, as interpolation depends on information on the physical element. However, dune-localfunctions does only have access to master element.

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