Error estimates for the convergence of a finite volume discretization of convection–diffusion equations
Jérôme Droniou · Journal of Numerical Mathematics · 2003
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 H 1+ s and the right-hand side is ƒ +div( G ) with ƒ ∈ L 2 and G ∈ ( H s ) N , then the solution of the finite volume scheme converges in discrete H 1 - norm to the exact solution, with a rate of convergence of order h s (where h is the size of the mesh).