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A stable finite element for the stokes equations

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Abstract

We present in this paper a new velocity-pressure finite element for the computation of Stokes flow. We discretize the velocity field with continuous piecewise linear functions enriched by bubble functions, and the pressure by piecewise linear functions. We show that this element satisfies the usual inf-sup condition and converges with first order for both velocities and pressure. Finally we relate this element to families of higer order elements and to the popular Taylor-Hood element.

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Authors and Affiliations

  1. Dept. of Mathematics, Univ. of Maryland, 20742, College Park, MD, U.S.A.

    D. N. Arnold

  2. Dip. Meccanica Strutturale, Univ. di Pavia, Italy

    F. Brezzi

  3. Istituto di Analisi Numerica del CNR di Pavia, Italy

    F. Brezzi

  4. Dép. Mathématique, Univ. Laval, G1K7P4, Québec, Canada

    M. Fortin

Authors
  1. D. N. Arnold
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  2. F. Brezzi
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  3. M. Fortin
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Arnold, D.N., Brezzi, F. & Fortin, M. A stable finite element for the stokes equations. Calcolo 21, 337–344 (1984). https://doi.org/10.1007/BF02576171

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  • DOI: https://doi.org/10.1007/BF02576171

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