A Posteriori Error Analysis of Any Order Finite Volume Methods for Elliptic Problems

A Posteriori Error Analysis of Any Order Finite Volume Methods for Elliptic Problems

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.

Author Details

Yuanyuan Zhang

Min Yang

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