Convergence Analysis for the Full-Upwind Finite Volume Solution of a Convection–Diffusion Problem

The paper is devoted to the study of convergence properties for an often used cell-centered full-upwind Finite Volume Method (FVM) with Voronoi boxes. This FVM is applied to a convection–diffusion problem. The approach to proving convergence of the FVM is based on the construction of a nonconforming Petrov–Galerkin Finite Element Method (FEM), such that the system of linear equations coincides completely with that of the FVM. Thus, by proving convergence properties of the FEM we obtain similar ones for the FVM. For the error estimation of the FEM the second Strang lemma has to be modified