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2011, Volume 2011: 1091-1100. Doi: 10.3934/proc.2011.2011.1091 open access
This issue Previous Article Gradient systems on networks Next Article Optimal control problems for quasi-variational inequalities and its numerical approximation

Constructing approximate solutions for three dimensional stationary Stokes flow

  • 1.

    Berufsakademie Nordhessen, University of Cooperative Education, Eichlerstr. 25, 34537 Bad Wildungen

  • 2.

    Fachbereich Mathematik, Universität Kassel, Heinrich Plett Str. 40 (AVZ), D-34132 Kassel

Received:  June 30, 2010
Revised:  January 31, 2011
Published:  August 2017
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    Abstract
  • In this article we develop a method for the numerical solution of a boundary value problem for the system of Stokes equations in three dimensions. Simultaneously we develop the method for linear splines and for quasi interpolants. For this we start with a representation of the uniquely determined velocity field $v$ by the double layer potential. In a fi rst step we approximate the kernel an the source density of the double layer potential. In a second step we use a collocation method for the determination of the unknown values of the source density in the collocation points. The convergence analysis is carried out and error estimates are given.
    Mathematics Subject Classification: Primary: 35Q30, 45B05; Secondary: 65M12, 76D07.

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