Constructing approximate solutions for three dimensional stationary Stokes flow

Pages: 1091 - 1100, Issue Special, September 2011

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Frank Müller - Berufsakademie Nordhessen, University of Cooperative Education, Eichlerstr. 25, 34537 Bad Wildungen, Germany (email)
Werner Varnhorn - Fachbereich Mathematik, Universität Kassel, Heinrich Plett Str. 40 (AVZ), D-34132 Kassel, Germany (email)

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.

Keywords:  Stokes equations, Boundary integral equation, Quasi interpolation
Mathematics Subject Classification:  Primary: 35Q30, 45B05; Secondary: 65M12, 76D07

Received: July 2010;      Revised: February 2011;      Published: October 2011.