Flux reconstruction and a posteriori error estimation for discontinuous Galerkin methods on general nonmatching grids

Abstract

Discontinuous Galerkin methods handle very well general polygonal and nonmatching meshes. We present in this Note a H ( div ) -conforming reconstruction of the flux on such meshes in the setting of an elliptic problem. We exploit the local conservation property of discontinuous Galerkin methods and solve local Neumann problems by means of the Raviart–Thomas–Nédélec mixed finite element method. Our reconstruction can be used in a guaranteed a posteriori error estimate and it is also of independent interest when the approximate flux is to be used subsequently in a transport problem. To cite this article: A. Ern, M. Vohralík, C. R. Acad. Sci. Paris, Ser. I 347 (2009).