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Numerische Mathematik

, Volume 44, Issue 2, pp 201–217 | Cite as

Combined finite element and spectral approximation of the Navier-Stokes equations

  • Claudio Canuto
  • Yvon Maday
  • Alfio Quarteroni
Article

Summary

We present a method for the numerical approximation of Navier-Stokes equations with one direction of periodicity. In this direction a Fourier pseudospectral method is used, in the two others a standard F.E.M. is applied. We prove optimal rate of convergence where the two parameters of discretization intervene independently.

Subject Classifications

AMS(MOS): 65N30 CR: 5.17 

Approximation des équations de Navier-Stokes par une méthode éléments finis-spectrale Fourier

Resumé

On présente une méthode d'approximation numérique des équations de Navier-Stokes possédant une direction de périodicité. Dans cette direction une méthode pseudospectrale basée sur des développements en série de Fourier est utilisée, dans les deux autres on applique une méthode d'éléments finis standard. On montre que la convergence est optimale et que les deux paramètres de discrétisation peuvent être choisis de façon indépendante.

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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Claudio Canuto
    • 1
  • Yvon Maday
    • 2
    • 3
  • Alfio Quarteroni
    • 1
  1. 1.Istituto di Analisi Numerica and Istituto di Matematica Applicata dell'Università di PaviaPaviaItalia
  2. 2.Analyse Numérique, Tour 55-65Université P. & M. CurieParis Cedex 05France
  3. 3.Université de Paris Val de MarneCreteil CedexFrance

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