A unified framework for a posteriori error estimation for the Stokes problem - Archive ouverte HAL Access content directly
Journal Articles Numerische Mathematik Year : 2012

A unified framework for a posteriori error estimation for the Stokes problem

(1) , (1) , (2)
1
2

Abstract

In this paper, a unified framework for a posteriori error estimation for the Stokes problem is developed. It is based on $[H^1_0(\Om)]^d$-conforming velocity reconstruction and $\HH(\dv,\Om)$-conforming, locally conservative flux (stress) reconstruction. It gives guaranteed, fully computable global upper bounds as well as local lower bounds on the energy error. In order to apply this framework to a given numerical method, two simple conditions need to be checked. We show how to do this for various conforming and conforming stabilized finite element methods, the discontinuous Galerkin method, the Crouzeix--Raviart nonconforming finite element method, the mixed finite element method, and a general class of finite volume methods. Numerical experiments illustrate the theoretical developments.
Fichier principal
Vignette du fichier
a_post_Stokes.pdf (1.39 Mo) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00470131 , version 1 (03-04-2010)
hal-00470131 , version 2 (28-01-2011)

Identifiers

Cite

Antti Hannukainen, Rolf Stenberg, Martin Vohralík. A unified framework for a posteriori error estimation for the Stokes problem. Numerische Mathematik, 2012, 122 (4), pp.725-769. ⟨10.1007/s00211-012-0472-x⟩. ⟨hal-00470131v2⟩
253 View
469 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More