I stumbled on this topic Defining subdomains from gmsh on CG elements - #2 by dokken where you say that " 1. Interpolate (not well defined) or project (well defined) the DG-0 data into a CG-1 space."
Does it mean that I can compute my heat flux qw safely in a CG1 space instead of DG0 using project?
Using https://github.com/michalhabera/dolfiny/blob/master/dolfiny/projection.py to make my own project function to perform qw = project(k*grad(T), V) I get the results below
which looks smoother than using
interpolate: