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T. Horger, J. Melenk, B. Wohlmuth:
"On optimal L2- and surface flux convergence in FEM";
in: "ASC Report 39/2014", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2014, ISBN: 978-3-902627-07-0, 1 - 26.

We show that optimal L2-convergence in the finite element method on
quasi-uniform meshes can be achieved if the underlying boundary value problem admits a shift theorem by more than 1/2. For this, 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.

L2 a priori bounds, shift theorem, reentrant corners

http://www.asc.tuwien.ac.at/preprint/2014/asc39x2014.pdf