dc.date.accessioned 2009-08-13T11:52:07Z dc.date.available 2009-08-13T11:52:07Z dc.date.issued 2009 dc.identifier.uri urn:nbn:de:hebis:34-2009081329429 dc.identifier.uri http://hdl.handle.net/123456789/2009081329429 dc.language.iso eng dc.rights Urheberrechtlich geschützt dc.rights.uri https://rightsstatements.org/page/InC/1.0/ dc.subject Stokes boundary value eng dc.subject.ddc 510 dc.title Approximate solutions and error estimates for a Stokes boundary value problem eng dc.type Preprint dcterms.abstract The aim of this paper is the numerical treatment of a boundary value eng 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. dcterms.accessRights open access dcterms.creator Müller, Frank dcterms.creator Varnhorn, Werner dcterms.isPartOf Mathematische Schriften Kassel ;; 09 , 02 ger dc.subject.msc 65M12 ger dc.subject.msc 65M15 ger dc.subject.msc 76D07 ger dcterms.source.journal Mathematische Schriften Kassel ger dcterms.source.volume 09 , 02
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