Titre :

A posteriori error estimator based on gradient recovery by averaging for convection-diffusion-reaction problems approximated by discontinuous Galerkin methods

Auteur(s) :

Creusé, Emmanuel [Auteur]
SImulations and Modeling for PArticles and Fluids [SIMPAF]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Nicaise, Serge [Auteur]
Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015 [LAMAV]

Titre de la revue :

IMA Journal of Numerical Analysis

Pagination :

212-241

Éditeur :

Oxford University Press (OUP)

Date de publication :

2013

ISSN :

0272-4979

Mot(s)-clé(s) :

Discontinuous Galerkin finite elements
Convection-diffusion-reaction problems
A posteriori estimator
Discontinuous Galerkin finite elements.

Discipline(s) HAL :

Mathématiques [math]/Analyse numérique [math.NA]

Résumé en anglais : [en]

We consider some (anisotropic and piecewise constant) convection-diffusion-reaction problems in domains of R2, approximated by a discontinuous Galerkin method with polynomials of any degree. We propose two a posteriori ...
Lire la suite >We consider some (anisotropic and piecewise constant) convection-diffusion-reaction problems in domains of R2, approximated by a discontinuous Galerkin method with polynomials of any degree. We propose two a posteriori error estimators based on gradient recovery by averaging. It is shown that these estimators give rise to an upper bound where the constant is explicitly known up to some additional terms that guarantees reliability. The lower bound is also established, one being robust when the convection term (or the reaction term) becomes dominant. Moreover, the estimator is asymptotically exact when the recovered gradient is superconvergent. The reliability and efficiency of the proposed estimators are confirmed by some numerical tests.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL