Constructing approximate solutions for three dimensional stationary Stokes flow

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2011, 2011(Special): 1091-1100. doi: 10.3934/proc.2011.2011.1091

Constructing approximate solutions for three dimensional stationary Stokes flow

Frank Müller ^1, and Werner Varnhorn ^2,

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

Received July 2010 Revised February 2011 Published October 2011

Abstract
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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 first 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.

Citation: Frank Müller, Werner Varnhorn. Constructing approximate solutions for three dimensional stationary Stokes flow. Conference Publications, 2011, 2011 (Special) : 1091-1100. doi: 10.3934/proc.2011.2011.1091

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