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Title: Artificial boundary conditions for the Stokes and Navier-Stokes equations in domains that are layer-like at infinity
Authors: Nazarov, Serguei A.Specovius-Neugebauer, Maria
???metadata.dc.subject.ddc???: 510 - Mathematik (Mathematics)
Issue Date: 2005
Publisher: Universität Kassel, FB 17, Mathematik/Informatik
Series/Report no.: Mathematische Schriften Kassel05, 08
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.
URI: urn:nbn:de:hebis:34-200604069073
Appears in Collections:Mathematische Schriften Kassel

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