dc.date.accessioned 2007-04-17T07:39:04Z dc.date.available 2007-04-17T07:39:04Z dc.date.issued 2007 dc.identifier.uri urn:nbn:de:hebis:34-2007041717711 dc.identifier.uri http://hdl.handle.net/123456789/2007041717711 dc.format.extent 148137 bytes dc.format.mimetype application/pdf dc.language.iso eng dc.subject Approximate approximations eng dc.subject boundary point method eng dc.subject Stokes potentials eng dc.subject.ddc 510 dc.title Approximate Approximations and a Boundary Point Method for the Linearized Stokes System eng dc.type Preprint dcterms.abstract The method of approximate approximations, introduced by Maz'ya [1], can also be used for the numerical solution of boundary integral equations. In this case, the matrix eng of the resulting algebraic system to compute an approximate source density depends only on the position of a finite number of boundary points and on the direction of the normal vector in these points (Boundary Point Method). We investigate this approach for the Stokes problem in the whole space and for the Stokes boundary value problem in a bounded convex domain G subset R^2, where the second part consists of three steps: In a first step the unknown potential density is replaced by a linear combination of exponentially decreasing basis functions concentrated near the boundary points. In a second step, integration over the boundary partial G is replaced by integration over the tangents at the boundary points such that even analytical expressions for the potential approximations can be obtained. In a third step, finally, the linear algebraic system is solved to determine an approximate density function and the resulting solution of the Stokes boundary value problem. Even not convergent the method leads to an efficient approximation of the form O(h^2) + epsilon, where epsilon can be chosen arbitrarily small. dcterms.accessRights open access dcterms.creator König, Sergej dcterms.creator Varnhorn, Werner dcterms.isPartOf Mathematische Schriften Kassel ger dcterms.isPartOf 07, 03 ger dc.subject.msc 31B10 eng dc.subject.msc 35J05 eng dc.subject.msc 41A30 eng dc.subject.msc 65N12 eng dc.subject.msc 76D07 eng
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