A posteriori error estimations of a SUPG method for anisotropic diffusion–convection–reaction problems

Abstract

This Note presents an a posteriori residual error estimator for diffusion–convection–reaction problems approximated by a SUPG scheme on isotropic or anisotropic meshes in R d , d = 2 or 3. This estimator is based on the jump of the flux and the interior residual of the approximated solution. It is constructed to work on anisotropic meshes which account for the eventual anisotropic behavior of the solution. The equivalence between the energy norm of the error and the estimator is proved. To cite this article: T. Apel, S. Nicaise, C. R. Acad. Sci. Paris, Ser. I 345 (2007).