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Analyse d'un élément mixte pour le problème de Stokes

I. Résultats généraux

Analysis of a mixed finite element for the Stokes problem

I. General results

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Summary

We consider some extensions of the classical error estimates for mixed problems. We take into account, in particular, nonconforming approximations and the splitting of the bilinear formb(·,·), intob 1(·,·) andb 2(·,·). We use this last fact to sharpen some estimates in a case where the forma(·,·) does not have coercivity in the right norm. We also consider duality results in the nonconforming case.

Résumé

Nous considérons quelques extensions des résultats classiques d'estimation d'erreur pour les problèmes mixtes. Nous étudions en particulier l'effet de l'emploi d'une approximation non conforme et celui de la décomposition de la formeb(·,·) enb 1(·,·) etb 2(·,·). Nous employons cette dćomposition pour affiner certaines estimations dans le cas où la formea(·,·) n'est pas coercive dans la bonne norme. Nous considérons aussi des résultats de dualité dans le cas non conforme.

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Authors and Affiliations

  1. Départment de Mathématiques, Université Laval, QC G1K 7P4, Québec, Canada

    M. Fortin

  2. Département de Mathématiques et Informatiques, Faculté des Sciences, Université Ibn Tofaïl, Kénitra, Maroc

    Z. Mghazli

Authors
  1. M. Fortin
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  2. Z. Mghazli
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Additional information

Ce travail a été réalisé grâce à des subventions du fonds FCAR et du CRSNG.

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Fortin, M., Mghazli, Z. Analyse d'un élément mixte pour le problème de Stokes. Numer. Math. 62, 149–160 (1992). https://doi.org/10.1007/BF01396224

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  • DOI: https://doi.org/10.1007/BF01396224

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