Weighted L-norm a Posteriori Error Estimation of Fem in Polygons

In this paper, we generalize well-known results for the L2-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 nonconvex. 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 L2-norms are derived. Furthermore, the performance of the proposed error estimators is illustrated with a series of numerical experiments.