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Approximate solutions and error estimates for a Stokes boundary value problem
Abstract
The 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.
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.
Citation
@article{urn:nbn:de:hebis:34-2009081329429,
author={Müller, Frank and Varnhorn, Werner},
title={Approximate solutions and error estimates for a Stokes boundary value problem},
year={2009}
}
0500 Oax 0501 Text $btxt$2rdacontent 0502 Computermedien $bc$2rdacarrier 1100 2009$n2009 1500 1/eng 2050 ##0##urn:nbn:de:hebis:34-2009081329429 3000 Müller, Frank 3010 Varnhorn, Werner 4000 Approximate solutions and error estimates for a Stokes boundary value problem / Müller, Frank 4030 4060 Online-Ressource 4085 ##0##=u http://nbn-resolving.de/urn:nbn:de:hebis:34-2009081329429=x R 4204 \$dPreprint 4170 Mathematische Schriften Kassel ;; 09 , 02 7136 ##0##urn:nbn:de:hebis:34-2009081329429
2009-08-13T11:52:07Z 2009-08-13T11:52:07Z 2009 urn:nbn:de:hebis:34-2009081329429 http://hdl.handle.net/123456789/2009081329429 eng Urheberrechtlich geschützt https://rightsstatements.org/page/InC/1.0/ Stokes boundary value 510 Approximate solutions and error estimates for a Stokes boundary value problem Preprint The 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. open access Müller, Frank Varnhorn, Werner Mathematische Schriften Kassel ;; 09 , 02 65M12 65M15 76D07 Mathematische Schriften Kassel 09 , 02
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Urheberrechtlich geschützt