A Posteriori Error Estimations of Some Cell Centered Finite Volume Methods for Diffusion-Convection-Reaction Problems

Abstract

This paper presents an a posteriori residual error estimator for diffusion-convection-reaction problems approximated by some cell centered finite volume methods on isotropic or aniso-tropic meshes in Rd, d=2 or 3. For that purpose we built a reconstructed approximation, which is an appropriate interpolant of the finite volume solution. The error is then the difference between the exact solution and this interpolant. The residual error estimator is based on the jump of the normal derivative of the interpolant. We then prove the equivalence between the energy norm of the error and the residual error estimator. Some numerical tests confirm our theoretical results.