A Posteriori Error Analysis of Any Order Finite Volume Methods for Elliptic Problems (Advances in Applied Mathematics and Mechanics, 2020)
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.