@Article{IJNAM-4-1,
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 = {<p style="text-align: justify;">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.</p>},
issn = {2617-8710},
doi = {https://doi.org/2007-IJNAM-853},
url = {https://global-sci.com/article/83760/weighted-l2-norm-a-posteriori-error-estimation-of-fem-in-polygons}
}