Spectral Method for Mixed Inhomogeneous Boundary Value Problems in Three Dimensions

Spectral Method for Mixed Inhomogeneous Boundary Value Problems in Three Dimensions

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.