Convergence of finite volume scheme for three dimensional Poisson's equation
Numerical Analysis
2014-06-20 v1 Analysis of PDEs
Abstract
We construct and analyze a finite volume scheme for numerical solution of a three-dimensional Poisson equation. This is an extension of a two-dimensional approach by Suli 1991. Here we derive optimal convergence rates in the discrete H^1 norm and sub-optimal convergence in the maximum norm, where we use the maximal available regularity of the exact solution and minimal smoothness requirement on the source term. We also find a gap in the proof of a key estimate in a reference in Suli 1991 for which we present a modified and completed proof. Finally, the theoretical results derived in the paper are justified through implementing some canonical examples in 3D.
Keywords
Cite
@article{arxiv.1406.5018,
title = {Convergence of finite volume scheme for three dimensional Poisson's equation},
author = {Mohammad Asadzadeh and Krzysztof Bartoszek},
journal= {arXiv preprint arXiv:1406.5018},
year = {2014}
}