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

This paper is devoted to the study of a posteriori error estimates for the scalar nonlinear convection-diffusion-reaction equation c(t) + del . (uf(c)) (D delc)+ lambdac = 0. The estimates for the error between the exact solution and an upwind finite volume approximation to the solution are derived in the L-1-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.