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Methodes d'elements finis mixtes pour les equations de stokes et de Navier-Stokes dans un polygone non convexe

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Abstract

We study a mixed finite element method for the steady-state Navier-Stokes equations in a polygon which is not necessarily convex. To take into account the signularities of the solution near the corners, we introduce weighted Sobolev spaces and prove the convergence of the method. The use of a non-uniformly regular family of triangulations allows us to get best error estimates.

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Authors and Affiliations

  1. Laboratoire d'Analyse Numérique (La 189), CNRS et Université de Paris VI, Tour 55-65-5ème étage-4, place Jussieu, 75230, Paris Cedex 05

    C. Bernardi

  2. UER de Mathématiques et Informatique, Laboratoire d'Analyse Numérique, CNRS et Université de Rennes I, Rennes-Beaulieu, 35042, Rennes Cedex

    G. Raugel

Authors
  1. C. Bernardi
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  2. G. Raugel
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Bernardi, C., Raugel, G. Methodes d'elements finis mixtes pour les equations de stokes et de Navier-Stokes dans un polygone non convexe. Calcolo 18, 255–291 (1981). https://doi.org/10.1007/BF02576359

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  • DOI: https://doi.org/10.1007/BF02576359

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