SPECTRAL METHOD FOR MIXED INHOMOGENEOUS BOUNDARY VALUE PROBLEMS IN THREE DIMENSIONS  

作　　者：Tianjun Wang Benyu Guo Wei Li 

机构地区：[1]Department of Mathematics, Henan University of Science and Technology, Luo Yang 471003, China [2]Department of Mathematics, Shanghai Normal University, Shanghai 200235, China Scientific Computing Key Laboratory of Shanghai Universities,Division of Computational Science of E-Institute of Shanghai Universities

出　　处：《Journal of Computational Mathematics》2012年第6期579-600,共22页计算数学（英文）

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 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.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.

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

分 类 号：O175.25[理学—数学] TP391.41[理学—基础数学]