Abstract
We propose a new domain decomposition method for the Stokes equations in two and three dimensions. The algorithm, we propose, is very similar to an algorithm which is obtained by a Richardson iteration for the Schur complement equation using a Neumann-Neumann preconditioner. A comparison of both methods with the help of a Fourier analysis shows clearly the advantage of the new approach. This has also been validated by numerical experiments.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Y. Achdou, P. L. Tallec, F. Nataf, and M. Vidrascu, )A domain decoposition preconditioner for an advection-diffusion problem), Comp.Meth. Appl.Mech. Engrg, 184 (2000), pp. 145–170.
M. Ainsworth and S. Sherwin, )Domain decomposition preconditioners for p and hp finite element approximations of Stokes equations), Comput. Methods Appl. Mech. Engrg., 175 (1999), pp. 243–266.
V. Dolean, F. Nataf, and G. Rapin, )New constructions of domain decomposition methods for systems of PDEs), C.R. Math. Acad. Sci. Paris, 340 (2005), pp. 693–696.
V. Dolean, F. Nataf, and G. Rapin, Deriving a new domain decomposition method for the Stokes equations unsing the Smith factorization, tech. rep., Georg-August University Göttingen, 2006. Submitted.
L. F. Pavarino and O. B. Widlund, Balancing Neumann-Neumann methods for incompressible Stokes equations, Comm. Pure Appl. Math., 55 (2002), pp. 302–335.
Y.-H. D. Roeck and P. L. Tallec, Analysis and test of a local domain decomposition preconditioner, in Proceedings of the Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations, R. Glowinski, Y. Kuznetsov, G. Meurant, J. Périaux, and O. B. Widlund, eds., Philadelphia, PA, 1991, SIAM, pp. 112–128.
P. L. Tallec and A. Patra, Non-overlapping domain decomposition methods for adaptive hp approximations of the Stokes problem with discontinuous pressure fields, Comput. Methods Appl. Mech. Engrg., 145 (1997), pp. 361–379.
J. T. Wloka, B. Rowley, and B. Lawruk, Boundary Value Problems for Elliptic Systems, Cambridge University Press, 1995.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer
About this paper
Cite this paper
Nataf, F., Rapin, G. (2007). Construction of a New Domain Decomposition Method for the Stokes Equations. In: Widlund, O.B., Keyes, D.E. (eds) Domain Decomposition Methods in Science and Engineering XVI. Lecture Notes in Computational Science and Engineering, vol 55. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34469-8_27
Download citation
DOI: https://doi.org/10.1007/978-3-540-34469-8_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34468-1
Online ISBN: 978-3-540-34469-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)