Contributions to Books:
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,
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
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.