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T. Horger, J. Melenk, B. Wohlmuth:
"On optimal L2- and surface flux onvergence in FEM (extended version)";
in: "ASC Report 02/2015", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2015, ISBN: 978-3-902627-08-7, 1 - 48.

We show that optimal L2- convergence in the infinite element method on
quasi-uniform meshes can be achieved if, for some s0 > 1/2, the boundary value problem has the mapping property H−1+s → H1+s for s ∈ [0, s0]. 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 fators) the optimal rate is obtained.

L2 a priori bounds · duality argument · reentrant corners

http://www.asc.tuwien.ac.at/preprint/2015/asc02x2015.pdf