A posteriori error estimator based on gradient recovery by averaging for discontinuous Galerkin methods

Emmanuel Creusé (1) , Serge Nicaise (2)

1 SIMPAF - SImulations and Modeling for PArticles and Fluids
2 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015

We consider some (anisotropic and piecewise constant) diffusion problems in domains of R^2, approximated by a discontinuous Galerkin method with polynomials of any fixed degree. We propose an a posteriori error estimator based on gradient recovery by averaging. It is shown that this estimator gives rise to an upper bound where the constant is one up to some additional terms that guarantee reliability. The lower bound is also established. Moreover these additional terms are negligible when the recovered gradient is super convergent. The reliability and efficiency of the proposed estimator in confirmed by some numerical tests.

Mots clés: A posteriori estimator; Discontinuous Galerkin finite elements

Domaines: Analyse numérique [math.NA]

Emmanuel Creusé, Serge Nicaise. A posteriori error estimator based on gradient recovery by averaging for discontinuous Galerkin methods. Journal of Computational and Applied Mathematics, 2010, 234 (10), pp.2903-2915. ⟨10.1016/j.cam.2010.03.027⟩. ⟨hal-00768641⟩