| Issue |
ESAIM: M2AN
Volume 45, Number 4, July-August 2011
|
|
|---|---|---|
| Page(s) | 675 - 696 | |
| DOI | https://doi.org/10.1051/m2an/2010070 | |
| Published online | 30 November 2010 | |
A non-overlapping domain decomposition method for continuous-pressure mixed finite element approximations of the Stokes problem*,**
1
Département de Mathématiques, Université de Jijel,
BP 98 Aouled Aissa, 18000 Jijel, Algeria.
2
Université de Toulouse, Institut Mathématique de Toulouse,
Département de Génie Mathématique, INSA de Toulouse, 135 avenue de Rangueil,
31077 Toulouse Cedex 4, France. This email address is being protected from spambots. You need JavaScript enabled to view it.
; This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
20
August
2009
Revised:
20
June
2010
Abstract
This study is mainly dedicated to the development and analysis of non-overlapping domain decomposition methods for solving continuous-pressure finite element formulations of the Stokes problem. These methods have the following special features. By keeping the equations and unknowns unchanged at the cross points, that is, points shared by more than two subdomains, one can interpret them as iterative solvers of the actual discrete problem directly issued from the finite element scheme. In this way, the good stability properties of continuous-pressure mixed finite element approximations of the Stokes system are preserved. Estimates ensuring that each iteration can be performed in a stable way as well as a proof of the convergence of the iterative process provide a theoretical background for the application of the related solving procedure. Finally some numerical experiments are given to demonstrate the effectiveness of the approach, and particularly to compare its efficiency with an adaptation to this framework of a standard FETI-DP method.
Mathematics Subject Classification: 76D07 / 65N55 / 65N30
Key words: Stokes equations / incompressible fluids / domain decomposition methods / non-overlapping domain decomposition methods / FETI-DP methods / cross points
The research of the first author was supported by a grant within the framework of the French-Algerian program PROFAS. He is indebted to the Department of Engineering Mathematics and to the Toulouse Mathematics Institute for their kind hospitality during the achievement of this work.
The authors would like to thank the anonymous reviewers for their thorough reading and their comments which contribute to improve the final appearance of this paper.
© EDP Sciences, SMAI, 2010
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.