Year: 2007
Author: Thomas P. Wihler
International Journal of Numerical Analysis and Modeling, Vol. 4 (2007), Iss. 1 : pp. 100–115
Abstract
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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2007-IJNAM-853
International Journal of Numerical Analysis and Modeling, Vol. 4 (2007), Iss. 1 : pp. 100–115
Published online: 2007-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: finite element methods a posteriori error analysis $L^2$-norm error estimation non-convex polygonal domains.