Convergence of finite volume scheme for a three-dimensional Poisson equation

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. UDC 517.9
1 Introduction Our motivation for the numerical study of the classical Poisson equation stems from its appearance in the coupled system of partial differential equations involving the Vlasov type equations [...]