Error estimates on the approximate finite volume solution of convection diffusion equations with general boundary conditions

We study here the convergence of a finite volume scheme for a diffusion convection equation on an open bounded set of R-d (d = 2 or 3) for which we consider Dirichlet, Neumann, or Robin boundary conditions. We consider unstructured meshes which include Voronoi or triangular meshes; we use for the diffusion term an "s points" (where s is the number of sides of each cell) finite volume scheme and for the convection term an upstream finite volume scheme. Assuming the exact solution at least in H-2 we prove error estimates ina discrete H-0(1) norm of order the size of the mesh. Discrete Poincare inequalities then allow one to prove error estimates in the L-2 norm.