Numerical analysis
A posteriori analysis of the Chorin–Temam scheme for Stokes equations
Comptes Rendus. Mathématique, Volume 351 (2013) no. 23-24, pp. 931-936.

We consider the Chorin–Temam scheme (the simplest pressure-correction projection method) for the time discretization of an unstationary Stokes problem in DRd (d=2,3) given μ,f,u0: (P) find (u,p) solution to u|t=0=u0, u|D=0 and:

utμΔu+p=f,divu=0on (0,T)×D.(1)
Inspired by the analyses of the Backward Euler scheme performed by C. Bernardi and R. Verfürth, we derive a posteriori estimators for the error on u in L2(0,T;L2(D))-norm. Our investigation is supported by numerical experiments.

On discrétise en temps, par le schéma Chorin–Temam, un problème de Stokes non stationnaire posé dans DRd (d=2,3), étant donnés μ,f,u0 : (P) trouver (u,p) solution de u|t=0=u0, u|D=0 et (1). En sʼinspirant des analyses de C. Bernardi et de R. Verfürth pour le schéma Euler rétrograde, nous construisons des estimateurs a posteriori pour lʼerreur commise sur u en norme L2(0,T;L2(D)). Notre étude est étayée par des expériences numériques.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2013.10.026
Boyaval, Sébastien 1, 2; Picasso, Marco 3

1 Université Paris-Est, Laboratoire dʼhydraulique Saint-Venant (École nationale des ponts et chaussées – EDF R&D – CETMEF), 78401 Chatou cedex, France
2 INRIA, MICMAC team project, Rocquencourt, France
3 MATHICSE, Station 8, École polytechnique fedérale de Lausanne, 1015 Lausanne, Switzerland
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Boyaval, Sébastien; Picasso, Marco. A posteriori analysis of the Chorin–Temam scheme for Stokes equations. Comptes Rendus. Mathématique, Volume 351 (2013) no. 23-24, pp. 931-936. doi : 10.1016/j.crma.2013.10.026. http://www.numdam.org/articles/10.1016/j.crma.2013.10.026/

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