Followup from "WIP: Resolve "GradientFluxAdapter problem""
The following discussion from !105 (merged) should be addressed:

@sospinar started a discussion: (+13 comments)
I'm having troubles with the
\mathcal{RT}_1
elements in 3D. For simplices, the jumps are quite high, while for cubes a local matrix is throwing an error saying that is singular. Not really sure how to proceed here...
Collected info
A single testing case for the flux reconstruction shows strongly increased flux jump residuals:
case  error 

2D_1_cube  < 1E17 
2D_2_cube  < 1E17 
2D_3_cube  < 1E17 
2D_1_simplex  < 1E17 
2D_2_simplex  < 1E17 
2D_3_simplex  < 1E17 
3D_1_cube  < 1E17 
3D_2_cube  < 1E17 
3D_3_cube  none 
3D_1_simplex  < 1E17 
3D_2_simplex  2.70125e11 
3D_3_simplex  < 1E17 
We have several sources of numerical inaccuracies
 In the DG cases, they come because values that should represent the same value are generated by different local matrices;
Ax=b
problems. In the evaluation of the fluxes, they come from the Piola transformation, which have the following operations:
auto J = e.geometry().jacobianInverseTransposed(x); //! Geometry dependent J.invert(); J.umtv(x,y); //! y += A^T x y /= J.determinant();
Proposal
Will forward this question to Prof. Bastian.