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Spectral Discretization of the Axisymmetric Vorticity, Velocity and Pressure Formulation of the Stokes Problem

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An Erratum to this article was published on 19 April 2011

Abstract

We consider the Stokes problem in a three-dimensional axisymmetric bounded domain with non standard conditions which involve the normal component of the velocity and tangential component of the vorticity. We reduce the three-dimensional problem into a two-dimensional one and we write a variational formulation of it with three independent unknowns: the vorticity, the velocity and the pressure. Then we propose a discretization by spectral methods which relies on this formulation. A detailed numerical analysis leads to optimal error estimates for the three unknowns and numerical experiments confirm the interest of the discretization.

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Authors and Affiliations

  1. Ecole Nationale des Sciences de l’informatique/LAMSIN, Campus universitaire El Manar, B.P. 244 El Manar II, 2092, Tunis, Tunisia

    Nehla Abdellatif

  2. Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia

    Nejmeddine Chorfi

  3. Institut préparatoire aux études d’ingénieurs El Manar, Campus universitaire El Manar, B.P. 244 El Manar II, 2092, Tunis, Tunisia

    Sihem Trabelsi

Authors
  1. Nehla Abdellatif
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  2. Nejmeddine Chorfi
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  3. Sihem Trabelsi
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Correspondence to Nejmeddine Chorfi.

Additional information

The research of N. Chorfi was supported by the King Saud University, D.S.F.P. Program.

An erratum to this article can be found at http://dx.doi.org/10.1007/s10915-011-9484-4

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Abdellatif, N., Chorfi, N. & Trabelsi, S. Spectral Discretization of the Axisymmetric Vorticity, Velocity and Pressure Formulation of the Stokes Problem. J Sci Comput 47, 419–440 (2011). https://doi.org/10.1007/s10915-010-9446-2

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  • DOI: https://doi.org/10.1007/s10915-010-9446-2

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