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

作者：Nazarov Serguei A^*; Specovius Neugebauer Maria

来源：Zeitschrift fur Analysis und Ihre Anwendungen, 2008, 27(2): 125-155.

DOI：10.4171/zaa/1348

• Stokes Problem in layers
• Navier-Stokes system
• artificial boundary conditions
• exact boundary conditions
• Steklov-Poincare operator

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.

• 出版日期2008