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