JournalszaaVol. 27, No. 2pp. 125–155

Artificial Boundary Conditions for the Stokes and Navier–Stokes Equations in Domains that are Layer-Like at Infinity

  • Sergei A. Nazarov

    Institute for Problems in Mechanical Engineering RAS, St. Petersburg, Russian Federation
  • Maria Specovius-Neugebauer

    Universität Kassel, Germany
Artificial Boundary Conditions for the Stokes and Navier–Stokes Equations in Domains that are Layer-Like at Infinity cover
Download PDF

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 vv^\infty, pp^\infty to the problems in the unbounded domain Ω\Omega the error vvRv^\infty-v^R, ppRp^\infty-p^R is estimated in H1(ΩR)H^1(\Omega_R) and L2(ΩR)L^2(\Omega_R), respectively. Here vRv^R, pRp^R are the approximating solutions on the truncated domain ΩR\Omega_R, the parameter RR controls the exhausting of Ω\Omega. The artificial boundary conditions involve the Steklov-Poincar\'{e} 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(RN)O(R^{-N}), where NN can be arbitrarily large.

Cite this article

Sergei A. Nazarov, Maria Specovius-Neugebauer, Artificial Boundary Conditions for the Stokes and Navier–Stokes Equations in Domains that are Layer-Like at Infinity. Z. Anal. Anwend. 27 (2008), no. 2, pp. 125–155

DOI 10.4171/ZAA/1348