Hi Joachim,
thanks a lot for the help! Yes so I am defining that h_f since I was trying to define something like specialcf.meshsize but for surfaces. I have read on the forum that specialcf.meshsize takes the ratio between the element area and the edge length, which is the correct h to use for anisotropic meshes (see here). The reason I tried a different one in that the convergence study on the second method, which is supposed to converge with first order, seemed to have a scaling problem on the h parameter that was solved by using that h_f.
In case NgSolve automatically does that already for surfaces then I fear there must be a bug in my code.
Alessandro