Error estimates for the convergence of a finite volume discretization of convection-diffusion equations

We study error estimates for a finite volume discretization of an elliptic equation. We prove that, for s ∈ [0,1], if the exact solution belongs to H1+s and the right-hand side is f + div(G) with f ∈ L2 and G ∈ (Hs)N , then the solution of the finite volume scheme converges in discrete H1norm to the exact solution, with a rate of convergence of order hs (where h is the size of the mesh).