On optimal L²- and surface flux convergence in FEM

We show that optimal the boundary value problem has the mapping property (Formula present)for (Formula present). The lack of full elliptic regularity in the dual problem has to be compensated by additional regularity of the exact solution. Furthermore, we analyze for a Dirichlet problem the approximation of the normal derivative on the boundary without convexity assumption on the domain. We show that (up to logarithmic factors) the optimal rate is obtained.