A nonoverlapping DDM for the nonstationary Navier-Stokes problem

We consider the nonstationary incompressible Navier-Stokes problem in a bounded domain. A semidiscretization in time followed by a linearization procedure lead to Oseen type problems. For an efficient solution we take advantage of a nonoverlapping domain decomposition method (DDM) with interface conditions of Robin type. Strong convergence of the DDM-iterations to the Oseen solution can be proven. Furthermore we apply an a-posteriori estimate which controls the error on the subdomains in terms of the jumps of the velocity across the interface. This may serve as a stopping criterion and gives some information how to choose a free parameter appearing in the interface condition. A stabilized FEM is used to derive a discrete version of the DDM and requires a modification of the method.