A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations

Abstract

This paper is devoted to the study of a posteriori error estinmates for the scalar nonlinear convection-diffusion-reaction equation Ct + ∇ · (uf(c)) - ∇ · (D∇c) + λc = 0. The estimates for the error between the exact solution and an upwind finite volume approximation to the solution are derived in the L1-norm, independent of the diffusion parameter D. The resulting a posteriori error estimate is used to define an grid adaptive solution algorithm for the finite volume scheme. Finally numerical experiments underline the applicability of the theoretical results.