How to compute the "change of surface" for facet integration in arbitrary dimensions? about gridap.jl

[santiagobadia]

My first intuition, compute the det of the Jacobian of the transformation with an extra row being the unit normal, and take absolute value. Given a manifold M of dimension d-1, the Jacobian of the map from R^ (d-1) into M provides a rectangular Jacobian of dim (d-1)xd. If we append the unique (up to the sign) normal vector, we have a squared Jacobian. If we take its determinant and absolute value, we have a measure of the "surface".

[santiagobadia]

Replace |det J| by sqrt(det J^T J)

[fverdugo]

Nice!

This is the missing generic implementation of function meas.

(I would keep our current specializations for squared jacobians and also for changes of surface in 2D and 3D)