Preprint
Artificial boundary conditions for the Stokes and Navier-Stokes equations in domains that are layer-like at infinity
Abstract
Artificial boundary conditions are presented to approximate solutions to Stokes- and Navier-Stokes problems in domains that are layer-like at infinity. Based on results about existence and asymptotics of the solutions v^infinity, p^infinity to the problems in the unbounded domain Omega the error v^infinity - v^R, p^infinity - p^R is estimated in H^1(Omega_R) and L^2(Omega_R), respectively. Here v^R, p^R are the approximating solutions on the truncated domain Omega_R, the parameter R controls the exhausting of Omega. The artificial boundary conditions involve the Steklov-Poincare operator on a circle together with its inverse and thus turn out to be a combination of local and nonlocal boundary operators. Depending on the asymptotic decay of the data of the problems, in the linear case the error vanishes of order O(R^{-N}), where N can be arbitrarily large.
Citation
@article{urn:nbn:de:hebis:34-200604069073,
author={Nazarov, Serguei A. and Specovius-Neugebauer, Maria},
title={Artificial boundary conditions for the Stokes and Navier-Stokes equations in domains that are layer-like at infinity},
year={2005}
}
0500 Oax 0501 Text $btxt$2rdacontent 0502 Computermedien $bc$2rdacarrier 1100 2005$n2005 1500 1/eng 2050 ##0##urn:nbn:de:hebis:34-200604069073 3000 Nazarov, Serguei A. 3010 Specovius-Neugebauer, Maria 4000 Artificial boundary conditions for the Stokes and Navier-Stokes equations in domains that are layer-like at infinity / Nazarov, Serguei A. 4030 4060 Online-Ressource 4085 ##0##=u http://nbn-resolving.de/urn:nbn:de:hebis:34-200604069073=x R 4204 \$dPreprint 4170 Mathematische Schriften Kassel ;; 05, 08 7136 ##0##urn:nbn:de:hebis:34-200604069073
2006-04-06T07:41:25Z 2006-04-06T07:41:25Z 2005 urn:nbn:de:hebis:34-200604069073 http://hdl.handle.net/123456789/200604069073 288442 bytes application/pdf eng Universität Kassel, FB 17, Mathematik/Informatik Urheberrechtlich geschützt https://rightsstatements.org/page/InC/1.0/ Stokes-Problem Navier-Stokes-Gleichung Randwertproblem Stokes Problem in layers Navier-Stokes system Artificial boundary conditions Steklov-Poincare operator 510 Artificial boundary conditions for the Stokes and Navier-Stokes equations in domains that are layer-like at infinity Preprint Artificial boundary conditions are presented to approximate solutions to Stokes- and Navier-Stokes problems in domains that are layer-like at infinity. Based on results about existence and asymptotics of the solutions v^infinity, p^infinity to the problems in the unbounded domain Omega the error v^infinity - v^R, p^infinity - p^R is estimated in H^1(Omega_R) and L^2(Omega_R), respectively. Here v^R, p^R are the approximating solutions on the truncated domain Omega_R, the parameter R controls the exhausting of Omega. The artificial boundary conditions involve the Steklov-Poincare operator on a circle together with its inverse and thus turn out to be a combination of local and nonlocal boundary operators. Depending on the asymptotic decay of the data of the problems, in the linear case the error vanishes of order O(R^{-N}), where N can be arbitrarily large. open access Nazarov, Serguei A. Specovius-Neugebauer, Maria Mathematische Schriften Kassel ;; 05, 08 76M99 76D05 35Q30 Mathematische Schriften Kassel 05, 08
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