Create subdomain and integrate over it

[dokken]

I have shown how to do this in the context of surface integrals at:

jorgensd/dolfinx_mpc/blob/2af8c962f94cf821ea273b568e0336f31cc43513/python/dolfinx_mpc/utils/mpc_utils.py#L47

Which is similar to legacy dolfin:

Obtain velocity normal to boundary

As the FacetNormal as implied by its name, is defined on each Facet, and not for each degree of freedom, you have to approximate the normal at the degrees of freedom (for instance at corners). For your particular case, the problem is that you are trying to interpolate an ComponentTensor, that is an expression using ufl syntax. To work around this, I would suggest using an UserExpression as follows: n = FacetNormal(mesh) # Interpolate mesh values into boundary function u_boundary = Function(D) …

or you could use any of the suggestions by @francesco-ballarin