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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	< 1E-17
2D_2_cube	< 1E-17
2D_3_cube	< 1E-17
2D_1_simplex	< 1E-17
2D_2_simplex	< 1E-17
2D_3_simplex	< 1E-17
3D_1_cube	< 1E-17
3D_2_cube	< 1E-17
3D_3_cube	none
3D_1_simplex	< 1E-17
3D_2_simplex	2.70125e-11
3D_3_simplex	< 1E-17

@sospinar:

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

@sospinar:

Will forward this question to Prof. Bastian.

How to test the implementation?

Related issues

See #65 (closed), !105 (merged)