Year: 2020
Author: Yuanyuan Zhang, Min Yang
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 2 : pp. 564–578
Abstract
In this paper, we construct and analyze the a posteriori error estimators for any order finite volume methods (FVMs) for solving the elliptic boundary value problems in $R^2$. We shall prove that the a posteriori error estimators yield the global upper and local lower bounds for the $H^1$-norm error of the corresponding FVMs. So that the a posteriori error estimators are equivalent to the true errors in a certain sense. Lots of numerical experiments are performed to illustrate the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2019-0012
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 2 : pp. 564–578
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Any order finite volume methods a posteriori error estimate.