How to use the smith factorization for domain decomposition methods applied to the stokes equations

Abstract

In this paper we demonstrate that the Smith factorization is a powerful tool to derive new domain decomposition methods for vector valued problems. Here, the factorization is applied to the two-dimensional Stokes system. The key idea is the transformation of the Stokes problem into a scalar bi-harmonic problem. We show how a proposed domain decomposition method for the bi-harmonic problem leads to an algorithm for the Stokes equations which inherits the convergence behavior of the scalar problem.