Schwarz Algorithms for Stokes-Stokes Coupling

In this article, we exhibit the behavior of the Schwarz algorithms for the Steady Stokes equation in the case of two unbounded subdomains at the continuous level. The Schwarz methods have received a lot of attention during the last decades with the vast development of parallel computing devices. Hermann Amandus Schwarz, a German analyst, is considered to be the pioneer of the Domain Decomposition methods. We will closely observe how the overlapping and non overlapping Schwarz methods work for the steady Stokes problem. This problem has immediate practical application, modeling the flow of an incompressible fluid. For the analysis, we rely on Fourier analysis techniques and we provide comparison of the exhibited methods.