ffc team mailing list archive

[Peter Brune <prbrune@xxxxxxxxx>]

The higher-order normal is the reference normal transformed by the Piola
transform.  Interestingly, it's actually easier to get the local facet
length out of this than it is to compute it "manually".  This is of course:

n_iso = (1 / |J_surface|) * J * n_ref (I might be missing an inverse... it's
getting late)

Anyways, you can normalize the normal computed here to get the local
jacobian determinant for the surface, because you can just use your
higher-order cell jacobian to get your normal going in the right "direction,
and of course it's... normalized, making life easier.  Two birds with one
stone.  This would mean that  facet integrals would need the corresponding
cell Jacobian, but that's the case with both affine and higher-order
normals.  Right now I'm doing this by appending a higher-order normal
function as well as higher-order coordinates to the form with a transformer.

Thoughts?

- Peter