Optimal convergence results for the Brezzi-Pitkäranta approximation of the Stokes problem: Exterior domains

• Autorzy: Serguei A. Nazarov , Maria Specovius-Neugebauer
• Języki publikacji: EN

Abstrakty

EN

This paper deals with a strongly elliptic perturbation for the Stokes equation in exterior three-dimensional domains Ω with smooth boundary. The continuity equation is substituted by the equation -ε²Δp + div u = 0, and a Neumann boundary condition for the pressure is added. Using parameter dependent Sobolev norms, for bounded domains and for sufficiently smooth data we prove $H^{5/2-δ}$ convergence for the velocity part and $H^{3/2-δ}$ convergence for the pressure to the solution of the Stokes problem, with δ arbitrarily close to 0. For an exterior domain the asymptotic behavior at infinity of the solutions to both problems has also to be taken into account. Although the usual Kondratiev theory cannot be applied to the perturbed problem, it is shown that the asymptotics of the solutions to the exterior Stokes problem and the solution to the perturbed problem coincide completely. For sufficiently smooth data an appropriate decay leads to the convergence of all main asymptotic terms as well as convergence in $H^{5/2-δ}_{loc}$ and $H^{3/2-δ}_{loc}$, respectively, of the remainder to the corresponding parts of the Stokes solution.

Kategorie tematyczne

• 35Q30: Navier-Stokes equations
• 76D07: Stokes and related (Oseen, etc.) flows

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2008
• Tom: 81
• Numer: 1
• Strony: 297-320

Daty

wydano

2008

Twórcy

autor

Serguei A. Nazarov

• Institute of Mechanical, Engineering Problems, V.O. Bol'shoy Pr. 61, 199178, St. Petersburg, Russia

autor

Maria Specovius-Neugebauer

• Fachbereich 17, Mathematik/Informatik, Universität Kassel, D-34109 Kassel, Germany

Identyfikatory

DOI

10.4064/bc81-0-20