dc.date.accessioned 2006-04-06T11:39:17Z dc.date.available 2006-04-06T11:39:17Z dc.date.issued 2005 dc.identifier.uri urn:nbn:de:hebis:34-200604069104 dc.identifier.uri http://hdl.handle.net/123456789/200604069104 dc.format.extent 132946 bytes dc.format.mimetype application/pdf dc.language.iso eng dc.publisher Universität Kassel, FB 17, Mathematik/Informatik eng dc.rights Urheberrechtlich geschützt dc.rights.uri https://rightsstatements.org/page/InC/1.0/ dc.subject Approximate approximations eng dc.subject Laplace equation eng dc.subject Dirichlet problem eng dc.subject Boundary integral equation eng dc.subject Approximationstheorie eng dc.subject Laplace-Gleichung eng dc.subject Dirichlet-Problem eng dc.subject Integralgleichung eng dc.subject.ddc 510 dc.title An approximation method using approximate approximations eng dc.type Preprint dcterms.abstract The aim of this paper is to 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 Laplace equation in two dimensions using approximate approximations. 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.accessRights open access dcterms.creator Müller, Frank dcterms.creator Varnhorn, Werner dcterms.isPartOf Mathematische Schriften Kassel eng dcterms.isPartOf 05, 11 eng dc.subject.msc 65N38 eng dc.subject.msc 45B05 eng dc.subject.msc 35J05 eng dcterms.source.journal Mathematische Schriften Kassel dcterms.source.volume 05, 11
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