Convergence of finite volume scheme for a three dimensional Poisson's equation.
Journal article, 2014
We construct and analyze a finite volume scheme for numerical solution of a three-dimensional Poisson equation. We derive optimal convergence rates in the discrete H1 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. The theoretical results are justified through implementing some canonical examples in 3D. Bibliography: 26 titles. Illustrations: 4 figures.