Year: 2012
Journal of Computational Mathematics, Vol. 30 (2012), Iss. 6 : pp. 579–600
Abstract
In this paper, we investigate spectral method for mixed inhomogeneous boundary value problems in three dimensions. Some results on the three-dimensional Legendre approximation in Jacobi weighted Sobolev space are established, which improve and generalize the existing results, and play an important role in numerical solutions of partial differential equations. We also develop a lifting technique, with which we could handle mixed inhomogeneous boundary conditions easily. As examples of applications, spectral schemes are provided for three model problems with mixed inhomogeneous boundary conditions. The spectral accuracy in space of proposed algorithms is proved. Efficient implementations are presented. Numerical results demonstrate their high accuracy, and confirm the theoretical analysis well.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1206-m3891
Journal of Computational Mathematics, Vol. 30 (2012), Iss. 6 : pp. 579–600
Published online: 2012-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Three-dimensional Legendre approximation in Jacobi weighted Sobolev space Lifting technique Spectral method for mixed inhomogeneous boundary value problems.
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