Journal article
Artificial boundary conditions for the Stokes and NavierStokes equations in domains that are layerlike at infinity
Publication Details
Authors:  Nazarov, S.; SpecoviusNeugebauer, M.

Journal:  Zeitschrift für Analysis und ihre Anwendungen 
Abstract
Artificial boundary conditions are presented to approximate solutions to Stokes and NavierStokes problems in domains that are layerlike 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 H1(Omega(R)) and L2(Omega(R)), respectively. Here VR 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 SteklovPoincare 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), where N can be arbitrarily large.