Preprint
Approximate Approximations and a Boundary Point Method for the Linearized Stokes System
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
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.
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.
Citation
@article{urn:nbn:de:hebis:34-2007041717711,
author={König, Sergej and Varnhorn, Werner},
title={Approximate Approximations and a Boundary Point Method for the Linearized Stokes System},
year={2007}
}
0500 Oax 0501 Text $btxt$2rdacontent 0502 Computermedien $bc$2rdacarrier 1100 2007$n2007 1500 1/eng 2050 ##0##urn:nbn:de:hebis:34-2007041717711 3000 König, Sergej 3010 Varnhorn, Werner 4000 Approximate Approximations and a Boundary Point Method for the Linearized Stokes System / König, Sergej 4030 4060 Online-Ressource 4085 ##0##=u http://nbn-resolving.de/urn:nbn:de:hebis:34-2007041717711=x R 4204 \$dPreprint 4170 Mathematische Schriften Kassel ;; 07, 03 7136 ##0##urn:nbn:de:hebis:34-2007041717711
<resource xsi:schemaLocation="http://datacite.org/schema/kernel-2.2 http://schema.datacite.org/meta/kernel-2.2/metadata.xsd"> 2007-04-17T07:39:04Z 2007-04-17T07:39:04Z 2007 urn:nbn:de:hebis:34-2007041717711 http://hdl.handle.net/123456789/2007041717711 148137 bytes application/pdf eng Urheberrechtlich geschützt https://rightsstatements.org/page/InC/1.0/ Approximate approximations boundary point method Stokes potentials 510 Approximate Approximations and a Boundary Point Method for the Linearized Stokes System Preprint 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 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. open access König, Sergej Varnhorn, Werner Mathematische Schriften Kassel ;; 07, 03 31B10 35J05 41A30 65N12 76D07 Mathematische Schriften Kassel 07, 03 </resource>
The following license files are associated with this item:
:Urheberrechtlich geschützt