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Utilisation de la méthode des éléments finis en mécanique des fluides, I

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Abstract

An analysis is made of the possibility of building divergence free elements for the approximation of the Navier-Stokes equations of an incomprensible fluid. Two types of appoximation are considered. In the first real divergence free elements are considered. Many examples are given and error bounds are derived. It is shown that 0 (h 4) precision can be obtained using fourth degree polynomials. In the second type of approximation the incompressibility condition is satisfied only in the average. Two and three dimensional examples are given, using respectively second and third order polynomials.

A possible numerical scheme is proposed for the case the steady-state linearized Stokes problem. Experimental evidence shows that it can be also used in the general non-linear case. Simple numerical results are presented for the cavity problem in two dimensions.

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Authors and Affiliations

  1. Département de mathématiques, Université Laval, Québec, Canada

    M. Fortin

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  1. M. Fortin
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Ce travail a été rendu possible en partie grâce à une subvention du Conseil National de la Recherche du Canada.

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Fortin, M. Utilisation de la méthode des éléments finis en mécanique des fluides, I. Calcolo 12, 405–441 (1975). https://doi.org/10.1007/BF02575757

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