Volume 4, Issue 1
Weighted $L^2$-Norm a Posteriori Error Estimation of FEM in Polygons

Int. J. Numer. Anal. Mod., 4 (2007), pp. 100-115.

Published online: 2007-04

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• 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.

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@Article{IJNAM-4-100, author = {Wihler , Thomas P.}, title = {Weighted $L^2$-Norm a Posteriori Error Estimation of FEM in Polygons}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2007}, volume = {4}, number = {1}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/853.html} }
TY - JOUR T1 - Weighted $L^2$-Norm a Posteriori Error Estimation of FEM in Polygons AU - Wihler , Thomas P. JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 100 EP - 115 PY - 2007 DA - 2007/04 SN - 4 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/853.html KW - finite element methods, a posteriori error analysis, $L^2$-norm error estimation, non-convex polygonal domains. AB -

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.

Thomas P. Wihler. (2019). Weighted $L^2$-Norm a Posteriori Error Estimation of FEM in Polygons. International Journal of Numerical Analysis and Modeling. 4 (1). 100-115. doi:
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