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Study of a Numerical Approach for a Transient Flow Problem in Porous Media

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Abstract

In this work, we deal with the numerical study of the new approximation method proposed in [7] for a transient flow problem in porous media. The stationary problem, obtained from a time discretization of this transient problem, is considered as an optimal shape design formulation. We prove the existence of the solution of the discrete optimal shape problem obtained from finite element discretization. We study the convergence and give numerical results showing the efficiency of the proposed approach.

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Authors and Affiliations

  1. Département de Mathématiques Appliquées et Informatique, Université Cadi-Ayyad, Faculté des Sciences et des Techniques de Beni-Mellal, B.P. 523, Beni-Mellal, Maroc

    A. Chakib

  2. Département de Mathématiques et Informatique, Université Mohamed V, Faculté des Sciences, B.P. 1014, Rabat, Maroc

    T. Ghemires

  3. Laboratoire de Mathématiques Jean Leray, Université de Nantes/CNRS UMR 6629, 2, rue de la Houssinière, B.P. 92208, F-44322, Nantes, France

    A. Nachaoui

Authors
  1. A. Chakib
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  2. T. Ghemires
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  3. A. Nachaoui
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Correspondence to A. Nachaoui.

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Chakib, A., Ghemires, T. & Nachaoui, A. Study of a Numerical Approach for a Transient Flow Problem in Porous Media. Numerical Algorithms 34, 229–243 (2003). https://doi.org/10.1023/B:NUMA.0000005403.59451.61

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  • DOI: https://doi.org/10.1023/B:NUMA.0000005403.59451.61

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