I am having a problem that was also mentioned at the accepted answer to this question by Wolfgang Bangerth. I need to calculate, as it was specified at the question at the link, F1 integral and for that I need to calculate u1 at gauss points of the new mesh but with a certain accuracy so I do not loose overall convergence of the scheme. I want to ask if anyone can give me a tip on how to do that? What I am currently doing is calculating "shape functions" at gauss points of the new mesh and multiplying u1 with those shape functions, but this makes my overall scheme loose convergence so I need to do it in a more accurate way.
Thanks in advance.