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

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

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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.

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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Authors and Affiliations

  1. Istituto di Analisi Numerica and Istituto di Matematica Applicata dell'Università di Pavia, I-27100, Pavia, Italia

    Claudio Canuto & Alfio Quarteroni

  2. Analyse Numérique, Tour 55-65, Université P. & M. Curie, 4 Place Jussieu, F-75230, Paris Cedex 05, France

    Yvon Maday

  3. Université de Paris Val de Marne, Avenue du Général de Gaulle, F-94010, Creteil Cedex, France

    Yvon Maday

Authors
  1. Claudio Canuto
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  2. Yvon Maday
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  3. Alfio Quarteroni
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Canuto, C., Maday, Y. & Quarteroni, A. Combined finite element and spectral approximation of the Navier-Stokes equations. Numer. Math. 44, 201–217 (1984). https://doi.org/10.1007/BF01410105

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