Weighted L^2-norm a posteriori error estimation of FEM in polygons
Thomas P. Wihler 11 Department of Mathematics & Statistics, McGill University, Montréal, Québec, Canada, H3A 2K6
Received by the editors July 6, 2005, and in revised form, September 10, 2005.
In this paper, we generalize well-known results for the L-2-norm a posteriori error estimation of finite element methods applied to linear elliptic problems in convex polygonal domains to the case where the polygons are non-convex An important factor in our analysis is the investigation of a suitable dual problem whose solution, due to the non-convexity of the domain, may exhibit corner singularities. In order to describe this singular behavior of the dual solution certain weighted Sobolev spaces are employed. Based on this framework, upper and lower a posteriori error estimates in weighted L(2)-norms are derived. Furthermore, the performance of the proposed error estimators is illustrated with a series of numerical experiments.
AMS subject classifications: 65N
Key words: finite element methods; a posteriori error analysis; L-2-norm error estimation; non-convex polygonal domains