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 - <p style="text-align: justify;">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 &nbsp;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.</p>