Title :

Anisotropic a posteriori error estimation for the mixed discontinuous Galerkin approximation of the Stokes problem

Author(s) :

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

Journal title :

Numerical Methods for Partial Differential Equations

Publisher :

Wiley

Publication date :

2006

ISSN :

0749-159X

English keyword(s) :

DG method
Error estimator
Anisotropic solution
Stretched elements
Stokes problem

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [en]

The paper presents a posteriori error estimates for the mixed discontinuous Galerkin approximation of the stationary Stokes problem. We consider anisotropic finite element discretizations, i.e. elements with very large ...
Show more >The paper presents a posteriori error estimates for the mixed discontinuous Galerkin approximation of the stationary Stokes problem. We consider anisotropic finite element discretizations, i.e. elements with very large aspect ratio. Our analysis covers two- and three-dimensional domains. Lower and upper error bounds are proved with minimal assumptions on the meshes. The lower error bound is uniform with respect to the mesh anisotropy. The upper error bound depends on a proper alignment of the anisotropy of the mesh which is a common feature of anisotropic error estimation. In the special case of isotropic meshes, the results simplify, and upper and lower error bounds hold unconditionally. The numerical experiments confirm the theoretical predictions and show the usefulness of the anisotropic error estimator.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL