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, AUT, 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.