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Approximate approximations for the Poisson and the Stokes equations
Zusammenfassung
The method of approximate approximations is based on generating functions representing an approximate partition of the unity, only. In the present paper this method is used for the numerical solution of the Poisson equation and the Stokes system in R^n (n = 2, 3). The corresponding approximate volume potentials will be computed explicitly in these cases, containing a one-dimensional integral, only. Numerical simulations show the efficiency of the method and confirm the expected convergence of essentially second order, depending on the smoothness of the data.
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@article{urn:nbn:de:hebis:34-2007032817552,
author={Samrowski, Tatiana S. and Varnhorn, Werner},
title={Approximate approximations for the Poisson and the Stokes equations},
year={2006}
}
0500 Oax 0501 Text $btxt$2rdacontent 0502 Computermedien $bc$2rdacarrier 1100 2006$n2006 1500 1/eng 2050 ##0##urn:nbn:de:hebis:34-2007032817552 3000 Samrowski, Tatiana S. 3010 Varnhorn, Werner 4000 Approximate approximations for the Poisson and the Stokes equations / Samrowski, Tatiana S. 4030 4060 Online-Ressource 4085 ##0##=u http://nbn-resolving.de/urn:nbn:de:hebis:34-2007032817552=x R 4204 \$dPreprint 4170 Mathematische Schriften Kassel ;; 06, 09 7136 ##0##urn:nbn:de:hebis:34-2007032817552
2007-03-28T11:32:24Z 2007-03-28T11:32:24Z 2006 urn:nbn:de:hebis:34-2007032817552 http://hdl.handle.net/123456789/2007032817552 193118 bytes application/pdf eng urn:nbn:de:hebis:2006110215417 Urheberrechtlich geschützt https://rightsstatements.org/page/InC/1.0/ Approximate approximations volume potentials Poisson equation Stokes system 510 Approximate approximations for the Poisson and the Stokes equations Preprint The method of approximate approximations is based on generating functions representing an approximate partition of the unity, only. In the present paper this method is used for the numerical solution of the Poisson equation and the Stokes system in R^n (n = 2, 3). The corresponding approximate volume potentials will be computed explicitly in these cases, containing a one-dimensional integral, only. Numerical simulations show the efficiency of the method and confirm the expected convergence of essentially second order, depending on the smoothness of the data. open access Samrowski, Tatiana S. Varnhorn, Werner Mathematische Schriften Kassel ;; 06, 09 31B10 35J05 41A30 65N12 76D07 Mathematische Schriften Kassel 06, 09
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