Boundary Quadrature elements

[pbrubeck]

Description

This PR adds support for Boundary Quadrature / BQ elements.

On triangles and tetrahedra, Quadrature elements do not represent polynomial spaces, as the number of quadrature points differs from the dimension of P_k. Therefore the degree of a Quadrature element is used as the degree of the integrand to be integrated exactly. On tensor product cells, the Quadrature element corresponds to the GL element, but the degrees will not match.

Whenever assembling forms with Quadrature or Boundary Quadrature elements, we use a quadrature matching the element degree, as opposed to the estimated quadrature degree.

We also add support for projection onto the BQ space using the same trace norm on the facets used by HDiv Trace. This facilitates computing the FacetNormal at quadrature points:

project(FacetNormal(mesh), VectorFunctionSpace(mesh, "BQ", degree))

Depends on firedrakeproject/fiat#126

[github-actions]

	Tests	Passed ✅	Skipped ⏭️	Failed ❌
Firedrake real	8197 ran	7484 passed	713 skipped	0 failed

[github-actions]

	Tests	Passed ✅	Skipped ⏭️	Failed ❌
Firedrake complex	8244 ran	6600 passed	1644 skipped	0 failed

[github-actions]

	Tests	Passed ✅	Skipped ⏭️	Failed ❌
Firedrake default	8285 ran	7583 passed	702 skipped	0 failed

[ksagiyam]

Reviewed during the meeting.