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《Chinese Journal of Engineering Mathematics》 2009-03
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A Schwarz Alternating Method for the Anisotropic Elliptic Boundary Value Problem on Unbounded Domains

ZHENG Quan, DONG Jun-yu, BAI Rong-xia (College of Sciences, North China University of Technology, Beijing 100144)  
This paper investigates a Schwarz alternating method, based on the finite element method and the natural boundary element method, for solving the anisotropic elliptic problem on unbounded domains. The domain infinity outside the elongated boundary is resolved and the diffculty of the small coeffcient is overcome by introducing elliptic artificial boundaries. Its geometric convergence is proved in the sense of 1-norm by using the projection theory. The Fourier analysis is used to derive an optimal convergence rate formula dependent upon the overlapping degree of subdomains, the lowest frequency of the exact solution and the anisotropic coeffcients. The numerical examples confirm the convergence theory and show their practical application.
【Fund】: 北京市自然科学基金(1072009);; 国家重点基础研究发展计划项目(2002CB312104)
【CateGory Index】: O241.82
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