Numerical solution of the Navier-Stokes equations by domain decomposition methods

We consider numerical approximations to the Navier-Stokes equations for viscous, incompressible flows in planar domains. We discuss two different kinds of domain decomposition techniques for the effective solution of the discrete problems. The former is based on enforcing iteratively the transmission conditions at subdomain interfaces. The latter moves from an Uzawa type algorithm that reduces the coupled problem to a simpler elliptic problem for the pressure field. For both approaches theoretical and computational aspects are analyzed.