A posteriori residual error estimation of a cell-centered finite volume method

We present an a posteriori residual error estimator for the Laplace equation using a cell-centered finite volume method in the plane. For that purpose we associate to the approximated solution 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. The equivalence between the discrete H¹-seminorm of the error and the residual error estimator is proved. The proof of the upper error bound uses the Helmholtz decomposition of the broken gradient of the error and some quasi-orthogonality relations. To cite this article: S. Nicaise, C. R. Acad. Sci. Paris, Ser. I 338 (2004).