Title :

A posteriori error estimation for the Stokes problem : Anisotropic and Isotropic discretizations

Author(s) :

Creusé, Emmanuel [Auteur]
SImulations and Modeling for PArticles and Fluids [SIMPAF]
Kunert, Gerd [Auteur]
Chemnitz University of Technology / Technische Universität Chemnitz
Nicaise, Serge [Auteur]
Laboratoire de Mathématiques Appliquées au Calcul Scientifique - EA 3337 [MACS]

Journal title :

Mathematical Models and Methods in Applied Sciences

Pages :

1297-1341

Publisher :

World Scientific Publishing

Publication date :

2004

ISSN :

0218-2025

English keyword(s) :

Error estimator
anisotropic solution
stretched elements
stokes problem

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

The paper presents a posteriori error estimators for the stationary Stokes problem. We consider anisotropic finite element discretizations (i.e. elements with very large aspect ratio) where conventional, isotropic error ...
Show more >The paper presents a posteriori error estimators for the stationary Stokes problem. We consider anisotropic finite element discretizations (i.e. elements with very large aspect ratio) where conventional, isotropic error estimators fail. Our analysis covers two- and three-dimensional domains, conforming and non-conforming discretizations as well as different elements. This large variety of settings requires different approaches and results in different estimators. Furthermore many examples of finite element pairs that are covered by the analysis are presented. Lower and upper error bounds form the main result with minimal assumptions on the elements. The lower error bound is uniform with respect to the mesh anisotropy with the exception of nonconforming 3D discretizations made of pentahedra or hexahedra. 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. Some of the corresponding results seem to be novel (in particular for 3D domains), and cover element pairs of practical importance. The numerical experiments confirm the theoretical predictions and show the usefulness of the anisotropic error estimators.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL