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Comptes Rendus Mathématique
Volume 334, n° 7
pages 603-608 (2002)
Doi : S1631-073X(02)02319-1
Received : 28 May 2001 ; 
A three field stabilized finite element method for the Stokes equations
Une méthode d'éléments finis stabilisée à trois champs pour les équations de Stokes

Mohamed Amara a , Eliseo Chacón Vera b , David Trujillo a
a IPRA-LMA, Université de Pau et des Pay de l'Adour, 64000 Pau, France 
b Departamento de ecuaciones diferenciales y analysis, Universidad de Sevilla, 41080 Sevilla, Spain 

Note presented by Philippe G. Ciarlet


We consider in this work the boundary value problem for Stokes equations on a two dimensional domain in cases where non-standard boundary conditions are given. We study the cases where pressure and normal or tangential components of the velocity are given in different parts of the boundary and solve the problem with a minimal regularity. We introduce the problem and its variational formulation which is a mixed one. The principal unknowns are the pressure and the vorticity, the multiplier is the velocity. We present the numerical discretization which needs some stabilization. We prove the convergence and the behavior of the a priori error estimates. Some numerical tests are also presented. To cite this article: M. Amara et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 603-608.

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On propose dans ce travail, une formulation vitesse-tourbillon-pression pour le problème de Stokes bidimensionnel dans lequel on impose des conditions au bord non standard. On s'intèresse plus précisément aux cas où, sur certaines parties du bord, sont données la pression et la composante tangentielle de la vitesse ou bien le tourbillon et la composante normale de la vitesse. En partant d'une formulation mixte variationnelle le problème est résolu avec des hypothèses minimales sur la régularité. Dans cette formulation, les inconnues principales sont la pression et le tourbillon, tandis que la vitesse joue le rôle du multiplicateur. Nous présentons le problème discrétisé associé, pour lequel nous rajoutons un terme de stabilisation. Un résultat de convergence, décrivant le comportement de l'erreur d'approximation a priori, est démontré. Nous terminons par quelques résultats numériques. Pour citer cet article : M. Amara et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 603-608.

The full text of this article is available in PDF format.

© 2002  Académie des sciences/Éditions scientifiques et médicales Elsevier SAS. All Rights Reserved.
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