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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Overlapping optimized Schwarz methods for parabolic equations in $ n$ dimensions


Author: Minh-Binh Tran
Journal: Proc. Amer. Math. Soc. 141 (2013), 1627-1640
MSC (2000): Primary 35K10, 65M12
Published electronically: October 17, 2012
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Abstract: We introduce in this paper a new tool to prove the convergence of the overlapping optimized Schwarz methods with multisubdomains. The technique is based on some estimates of the errors on the boundaries of the overlapping strips. Our guiding example is an $ n$-dimensional linear parabolic equation.


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Additional Information

Minh-Binh Tran
Affiliation: Basque Center for Applied Mathematics (BCAM), Alameda de Mazarredo, 14, E-48009 Bilbao, Basque Country, Spain
Email: tbinh@bcamath.org

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11522-9
PII: S 0002-9939(2012)11522-9
Keywords: Partial differential equations, domain decomposition methods.
Received by editor(s): September 25, 2010
Received by editor(s) in revised form: June 6, 2011, and September 1, 2011
Published electronically: October 17, 2012
Additional Notes: The author has been partially supported by the ERC Advanced Grant FP7-246775 NUMERIWAVES
Communicated by: Matthew J. Gursky
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.