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

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.

added feature label

mentioned in merge request !70 (merged)

mentioned in commit e3df56c3

Hi Jakub, I just submitted the BDM part as a separate merge request (!97 (merged)). Would you agree that all relevant parts of this MR are either merged or moved to separate MR? Can I close this MR?

Thanks again for submitting the code.

Indeed, RT and BDM bases are merged or moved. Only the specific evaluation of global grid functions defined via an HDiv-basis is not included. But I guess this should be resolved differently anyway. Hence, MR can be closed.

closed

mentioned in commit 74e30b38

mentioned in commit lasse.hinrichsen/dune-functions@1ba79f04

mentioned in commit lasse.hinrichsen/dune-functions@e4e10789