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Volume 30, Issue 6
Spectral Method for Mixed Inhomogeneous Boundary Value Problems in Three Dimensions

Tianjun Wang, Benyu Guo & Wei Li

DOI: 10.4208/jcm.1206-m3891

J. Comp. Math., 30 (2012), pp. 579-600.

Published online: 2012-12

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  • 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.

  • Keywords

Three-dimensional Legendre approximation in Jacobi weighted Sobolev space, Lifting technique, Spectral method for mixed inhomogeneous boundary value problems.

  • AMS Subject Headings

65N35, 65M70, 41A10, 35J57, 35K51.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-30-579, author = {Tianjun Wang, Benyu Guo and Wei Li}, title = {Spectral Method for Mixed Inhomogeneous Boundary Value Problems in Three Dimensions}, journal = {Journal of Computational Mathematics}, year = {2012}, volume = {30}, number = {6}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1206-m3891}, url = {http://global-sci.org/intro/article_detail/jcm/8453.html} }
TY - JOUR T1 - Spectral Method for Mixed Inhomogeneous Boundary Value Problems in Three Dimensions AU - Tianjun Wang, Benyu Guo & Wei Li JO - Journal of Computational Mathematics VL - 6 SP - 579 EP - 600 PY - 2012 DA - 2012/12 SN - 30 DO - http://doi.org/10.4208/jcm.1206-m3891 UR - https://global-sci.org/intro/article_detail/jcm/8453.html KW - Three-dimensional Legendre approximation in Jacobi weighted Sobolev space, Lifting technique, Spectral method for mixed inhomogeneous boundary value problems. AB -

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.

Tianjun Wang, Benyu Guo and Wei Li. (2012). Spectral Method for Mixed Inhomogeneous Boundary Value Problems in Three Dimensions. Journal of Computational Mathematics. 30 (6). 579-600. doi:10.4208/jcm.1206-m3891
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