J. Korean Math. Soc. 2013; 50(6): 1291-1310
Printed November 1, 2013
https://doi.org/10.4134/JKMS.2013.50.6.1291
Copyright © The Korean Mathematical Society.
Byeong-Chun Shin
Chonnam National University
This paper develops least-squares pseudo-spectral collocation methods for elliptic boundary value problems having interface conditions given by discontinuous coefficients and singular source term. From the discontinuities of coefficients and singular source term, we derive the interface conditions and then we impose such interface conditions to solution spaces. We define two types of discrete least-squares functionals summing discontinuous spectral norms of the residual equations over two sub-domains. In this paper, we show that the homogeneous least-squares functionals are equivalent to appropriate product norms and the proposed methods have the spectral convergence. Finally, we present some numerical results to provide evidences for analysis and spectral convergence of the proposed methods.
Keywords: Pseudo-spectral method, least-squares method, interface prob\-lem
MSC numbers: Primary 65F10, 65F30
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