A posteriori error estimations of some cell-centered finite volume methods

Abstract

This paper presents the natural framework to residual based a posteriori error estimation of some cell-centered finite volume methods for the Laplace equation in $\R^d, d=2$ or 3. For that purpose we associate with the finite volume solution a reconstructed approximation, which is a kind of Morley interpolant. The error is then the difference between the exact solution and this Morley interpolant. The residual error estimator is based on the jump of normal and tangential derivatives of the Morley interpolant. We then prove the equivalence between the discrete H1 seminorm of the error and the residual error estimator. Numerical tests confirm our theoretical results.