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On Monotone and Schwarz Alternating Methodsfor Nonlinear Elliptic PDEs

Published online by Cambridge University Press:  15 April 2002

Shiu-Hong Lui
Shiu-Hong Lui*
Affiliation:
Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong. ([email protected])
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Abstract

The Schwarz alternating method can be used to solveelliptic boundary value problems on domains which consist of two or moreoverlapping subdomains. The solution is approximated by an infinite sequence offunctions which results from solving a sequence of elliptic boundary value problems in each of the subdomains. In this paper, proofs of convergence of some Schwarz alternating methods fornonlinear elliptic problems which are known to have solutions by the monotonemethod (also known as the method of subsolutions and supersolutions) aregiven. In particular, an additive Schwarz method for scalar as well as somecoupled nonlinear PDEs are shown to converge for finitely many subdomains.These results are applicable to several models in population biology.

Keywords

Domain decompositionnonlinear elliptic PDESchwarz alternating methodmonotone methodssubsolutionsupersolution.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 , Issue 1 , January 2001 , pp. 1 - 15
Copyright
© EDP Sciences, SMAI, 2001

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