SPECTRAL METHOD FOR MIXED INHOMOGENEOUS BOUNDARY VALUE PROBLEMS IN THREE DIMENSIONS

In this paper, we investigate spectral method for mixed inhomogeneous boundary value problems in three dimensions. Some results on the three-dimensional Legendre approxima- tion in Jacobi weighted Sobolev space are established, which improve and generalize the existing results, and play an important...

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Bibliographic Details
Published inJournal of computational mathematics Vol. 30; no. 6; pp. 579 - 600
Main Authors Wang, Tianjun, Guo, Benyu, Li, Wei
Format Journal Article
LanguageEnglish
Published Chinese Academy of Mathematices and System Sciences (AMSS) Chinese Academy of Sciences 01.11.2012
Subjects
Approximation
Boundary conditions
Boundary value problems
Computational mathematics
Integers
Interpolation
Mathematical functions
Sobolev spaces
Spectral methods
三维空间
偏微分方程数值解
加权Sobolev空间
混合边值问题
混合边界条件
谱方法
非均匀
非齐次边界条件
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Summary:In this paper, we investigate spectral method for mixed inhomogeneous boundary value problems in three dimensions. Some results on the three-dimensional Legendre approxima- tion 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 inho- mogeneous 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.
Bibliography:In this paper, we investigate spectral method for mixed inhomogeneous boundary value problems in three dimensions. Some results on the three-dimensional Legendre approxima- tion 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 inho- mogeneous 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.
Three-dimensional Legendre approximation in Jacobi weighted Sobolev space,Lifting technique, Spectral method for mixed inhomogeneous boundary value problems.
11-2126/O1
ISSN:0254-9409
1991-7139
DOI:10.4208/jcm.1206-m3891