TY - JOUR
T1 - A Posteriori Error Analysis of Any Order Finite Volume Methods for Elliptic Problems
AU - Zhang , Yuanyuan
AU - Yang , Min
JO - Advances in Applied Mathematics and Mechanics
VL - 2
SP - 564
EP - 578
PY - 2020
DA - 2020/01
SN - 12
DO - http://doi.org/10.4208/aamm.OA-2019-0012
UR - https://global-sci.org/intro/article_detail/aamm/13634.html
KW - Any order finite volume methods, a posteriori error estimate.
AB - <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>