@Article{AAMM-12-2,
author = {Zhang, Yuanyuan and Yang, Min},
title = {A Posteriori Error Analysis of Any Order Finite Volume Methods for Elliptic Problems},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2020},
volume = {12},
number = {2},
pages = {564--578},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2019-0012},
url = {https://global-sci.com/article/73046/a-posteriori-error-analysis-of-any-order-finite-volume-methods-for-elliptic-problems}
}