Aufsatz in einer Fachzeitschrift
Artificial boundary conditions for the Stokes and Navier-Stokes equations in domains that are layer-like at infinity
Details zur Publikation
Autor(inn)en: | Nazarov, S.; Specovius-Neugebauer, M. |
Publikationsjahr: | 2008 |
Zeitschrift: | Zeitschrift für Analysis und ihre Anwendungen |
Seitenbereich: | 125-155 |
Jahrgang/Band : | 27 |
Erste Seite: | 125 |
Letzte Seite: | 155 |
ISSN: | 0232-2064 |
DOI-Link der Erstveröffentlichung: |
Zusammenfassung, 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.
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.
