Default degree 3 quadrature on triangle inefficient?

[Miklós Homolya]

FIAT has generic rules for generating arbitrary order collapsed quadrature on triangles and tetrahedra ("canonical"). It also has a few hand-written rules for low-order quadrature on triangles and tetrahedra ("default"), which are presumably more efficient. The default rules indeed have fewer quadrature points than the canonical ones in all cases except one: degree 3 quadrature on the triangle.

The default scheme uses 6-point quadrature in this case, while the canonical scheme only uses 2 x 2 = 4 points.

[Lawrence Mitchell]

I note that the Strang-Fix scheme (the canonical one) is a symmetric quadrature rule, whereas the four-point collapsed quadrature is non-symmetric. This may or may not be an issue.