On Schwarz alternating methods for the incompressible Navier-Stokes equations

The Schwarz alternating method can be used to solve linear elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an infinite sequence of functions which result from solving a sequence of elliptic boundary value problems in each of the subdomains. This paper considers four Schwarz alternating methods for the N-dimensional, steady, viscous, incompressible Navier Stokes equations, N less than or equal to 4. It is shown that the Schwarz sequences converge to the true solution provided that the Reynolds number is sufficiently small.