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dc.rightsUrheberrechtlich geschützt
dc.subjectStokes boundary valueeng
dc.titleApproximate solutions and error estimates for a Stokes boundary value problemeng
dcterms.abstractThe aim of this paper is the numerical treatment of a boundary value problem for the system of Stokes' equations. For this we extend the method of approximate approximations to boundary value problems. This method was introduced by V. Maz'ya in 1991 and has been used until now for the approximation of smooth functions defined on the whole space and for the approximation of volume potentials. In the present paper we develop an approximation procedure for the solution of the interior Dirichlet problem for the system of Stokes' equations in two dimensions. The procedure is based on potential theoretical considerations in connection with a boundary integral equations method and consists of three approximation steps as follows. In a first step the unknown source density in the potential representation of the solution is replaced by approximate approximations. In a second step the decay behavior of the generating functions is used to gain a suitable approximation for the potential kernel, and in a third step Nyström's method leads to a linear algebraic system for the approximate source density. For every step a convergence analysis is established and corresponding error estimates are given.eng
dcterms.accessRightsopen access
dcterms.creatorMüller, Frank
dcterms.creatorVarnhorn, Werner
dcterms.isPartOfMathematische Schriften Kassel ;; 09 , 02ger
dcterms.source.journalMathematische Schriften Kasselger
dcterms.source.volume09 , 02

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