, Volume 32, Issue 4, pp 393-429
Date: 20 Dec 2008

Composite Laguerre-Legendre spectral method for exterior problems

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In this paper, we propose a composite Laguerre-Legendre spectral method for two-dimensional exterior problems. Results on the composite Laguerre-Legendre approximation, which is a set of piecewise mixed approximations coupled with domain decomposition, are established. These results play important roles in the related spectral methods for exterior problems. As examples of applications, the composite spectral schemes are provided for two model problems, with the convergence analysis. An efficient implementation is described. Numerical results demonstrate the spectral accuracy in space of this new approach, and confirm the analysis. The approximation results and techniques developed in this paper are also applicable to other problems defined on unbounded domains.

Communicated by Yuesheng Xu.
The work of Ben-yu Guo is supported in part by NSF of China N.10871131, The Science and Technology Commission of Shanghai Municipality, Grant N.075105118, Shanghai Leading Academic Discipline Project N.S30405 and Fund for E-institute of Shanghai Universities N.E03004.
The work of Tian-jun Wang is supported in part by NSF of China N.10871131 and The Doctor Fund of Henan University of Science and Technology N.09001263.