American Institute of Mathematical Sciences

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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

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.
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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