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

Dolean, Victorita and Nataf, Frédéric and Rapin, Gerd (2008) How to use the smith factorization for domain decomposition methods applied to the stokes equations. In: Domain Decomposition Methods in Science and Engineering XVII. Lecture Notes in Computational Science and Engineering, 60 . Springer, pp. 477-484. ISBN 9783540751984

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    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.