SPECTRAL METHOD FOR MIXED INHOMOGENEOUS BOUNDARY VALUE PROBLEMS IN THREE DIMENSIONS

被引：9

作者：

Wang, Tianjun ^{[1
]}

Guo, Benyu ^{[2
,3
]}

Li, Wei ^{[1
]}

机构：

[1] Henan Univ Sci & Technol, Dept Math, Luoyang 471003, Peoples R China

[2] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

[3] E Inst Shanghai Univ, Sci Comp Key Lab Shanghai Univ, Div Computat Sci, Shanghai, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL MATHEMATICS | 2012年 / 30卷 / 06期

关键词：

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

D O I：

10.4208/jcm.1206-m3891

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：579 / 600

页数：22

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