Xiao-Gimbutas quadrature (used in QuadratureSimplexElementGroup) not working properly

A QuadratureSimplexElementGroup Discretization does not correctly integrate the area of a square for 1st, 2nd, or 4th order (though 3rd seems to work).

Here's a test that verifies that the quadratures themselves do what they advertise to do.

https://gitlab.tiker.net/inducer/modepy/blob/master/test/test_quadrature.py#L69

Do you have a self-contained bit of code that demonstrates the issue you're seeing? (Ideally in the form of a test that I could add.)

FWIW, this bug likely belongs in either meshmode or modepy. I'll move it there once we figure out where the problem is.

With this, you now get the following error message:

meshmode.discretization.NoninterpolatoryElementGroupError: QuadratureSimplexElementGroup does not support interpolation because it is not unisolvent (its unit node count does not match its number of basis functions). Differentiation requires the ability to interpolate.

closed via commit e2a1afc5