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A priori and a posteriori estimates for three-dimensional Stokes equations with nonstandard boundary conditions

Authors

  • Hyam Abboud,

    1. Département de mathématiques, Faculté des Sciences II, Université Libanaise, Fanar-Maten, Liban
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  • Fida El Chami,

    1. Département de mathématiques, Faculté des Sciences II, Université Libanaise, Fanar-Maten, Liban
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  • Toni Sayah

    Corresponding author
    1. Département de mathématiques, Faculté des Sciences, Université Saint-Joseph, B.P 11-514 Riad El Solh, Beyrouth 1107 2050, Liban
    • Département de mathématiques, Faculté des Sciences, Université Saint-Joseph, B.P 11-514 Riad El Solh, Beyrouth 1107 2050, Liban
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Abstract

In this article, we study the Stokes problem with some nonstandard boundary conditions. The variational formulation decouples into a system for the velocity and a Poisson equation for the pressure. The corresponding discrete system do not need an inf-sup condition. Hence, the velocity is approximated with “curl” conforming finite elements and the pressure with standard continuous elements. Next, we establish optimal a priori and a posteriori estimates and we finally concluded with numerical tests. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2012

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