Error estimates for a combined finite volume-finite element method for nonlinear convection-diffusion problems

The subject of this paper is the analysis of error estimates of the combine d finite volume-finite element (FV-FE) method for the numerical solution of a scalar nonlinear conservation law equation with a diffusion term. Nonlin ear convective terms are approximated with the aid of a monotone finite vol ume scheme considered over the finite volume mesh dual to a triangular grid , whereas the diffusion term is discretized by piecewise linear conforming triangular finite elements. Under the assumption that the exact solution po ssesses some regularity properties and the triangulations are of a weakly a cute type, with the aid of the discrete maximum principle and a priori esti mates, error estimates of the method are proved.