Convergence analysis for an exponentially fitted finite volume method

The paper is devoted to the convergence analysis of a well-known cell-cente red Finite Volume Method (FVM) for a convection-diffusion problem in R-2. T his FVM is based on Voronoi boxes and exponential fitting. To prove the con vergence of the FVM, we use a new nonconforming Petrov Galerkin Finite Elem ent Method (FEM) for which the system of linear equations coincides complet ely with that of the FVM. Thus, by proving convergence properties of the FE M we obtain similar ones for the FVM. For the error estimation of the FEM w ell-known statements have to be modified.