Title :

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

Author(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]

Journal title :

IMA Journal of Numerical Analysis

Pages :

212-241

Publisher :

Oxford University Press (OUP)

Publication date :

2013

ISSN :

0272-4979

Keyword(s) :

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

HAL domain(s) :

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

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL