Journal article
Artificial boundary conditions for the Stokes and Navier-Stokes equations in domains that are layer-like at infinity



Publication Details
Authors:
Nazarov, S.; Specovius-Neugebauer, M.
Publication year:
2008
Journal:
Zeitschrift für Analysis und ihre Anwendungen
Pages range:
125-155
Volume number:
27
Start page:
125
End page:
155
ISSN:
0232-2064

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.


Research Areas


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