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Draft: Add some improved quadrature rules for the simplex elements

Simon Praetorius requested to merge feature/simplex-quadraturerules into master

Summary

We have some very old quadrature rules implemented for the simplex geometry types. In some cases there exist now rules with a lower number of points. And there are higher degree rules explicitly available, without relying on the Duffy transformed tensor-product rules. The MR adds some quadrature rules extracted from the literature.

Note, the rules are automatically generated, using a script in the dune-quadrature module (still experimental).

New quadrature rules

  • Simplex 2d: orders 1 - 25 (before only up to 12)
  • Simplex 3d: orders 1 - 10 (before only up to 5)
  • Quadrature points and weights are given in high precision using the DUNE_NUMBER_FROM_STRING macro.

ToDo

  • Some old rules could be preserved if they are not worse than the added new rules.
  • Add a changelog entry
Edited by Simon Praetorius

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