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Numerical analysis for backward Euler spectral discretization for Stokes equations with boundary conditions involving the pressure: part I

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Abstract

In this paper, we address the study of the time-dependent Stokes system with boundary conditions involving the pressure. We obtain existence and uniqueness for a class of Lipschitz-continuous domains. Next, a spectral discretizations of the problem is proposed combined with the backward Euler scheme. The discrete spaces are defined in a way to give exactly divergence-free discrete approximations for the velocity. Then, we prove the associated discrete inf–sup condition and derive a priori error estimates. Finally, some numerical experiments are presented.

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Authors and Affiliations

  1. Laboratoire Analyse, Optimisation et Traitement de l’information, University of Mohammed Seddik Ben Yahia, Ouled Aissa, B.P. 98, 18000, Jijel, Algeria

    O. Boussoufa & Y. Daikh

  2. Léonard de Vinci Pôle Universitaire, Research Center, 92 916, Paris La Défense, France

    D. Yakoubi

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  1. O. Boussoufa
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  2. Y. Daikh
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  3. D. Yakoubi
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Correspondence to D. Yakoubi.

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Boussoufa, O., Daikh, Y. & Yakoubi, D. Numerical analysis for backward Euler spectral discretization for Stokes equations with boundary conditions involving the pressure: part I. Calcolo 60, 25 (2023). https://doi.org/10.1007/s10092-023-00520-w

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  • DOI: https://doi.org/10.1007/s10092-023-00520-w

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