Some Improvements of the Order of the Convergence of Finite Volume Solutions

Abstract

In this article, we improve the order of the convergence of some finite volume solutions approximating some second order elliptic problems. In one dimensional space, we prove that finite volume approximations of order O(h), with k integer, can be obtained after k correction using the same scheme of three points and changing only the second members of the original system. This is done for general smooth second order elliptic problems. These results can be extended for non linear second order equation u = f(x, u, u) where f is a smooth function . In two dimensional space, we prove that finite volume approximation of order O(h) can be obtained, starting with finite volume solution of order O(h), by using the same matrix and changing only the second member of the original system. This is done for second order elliptic problems of the form −∆u + pu = f , with Dirichlet condition. These results can be extended to obtain finite volume approximation of order O(h). Heart idea behind these results is the one of Fox’s difference correction in the context of finite difference method.

9 Figures and Tables

Cite this paper

@inproceedings{Atfeh2004SomeIO, title={Some Improvements of the Order of the Convergence of Finite Volume Solutions}, author={Bilal Atfeh}, year={2004} }