Paper Info
Title
New space-time spectral and structured spectral element methods for high order problems.
Abstract
We propose new space–time spectral and structured spectral element methods for high order problems. By matrix decomposition, we introduce a family of new basis functions which leads to a diagonal system for the fourth order problems with constant coefficients. Based on new basis functions in space and a dual-Petrov–Galerkin formulation in time, we propose a new space–time spectral method for a time-dependent problem, and proved their spectral accuracy both in space and time. Numerical results demonstrate their high efficiency and coincide well with theoretical analysis. Further, to ultimately promote the numerical performance and efficiency, we exploit the idea of locally simultaneous diagonalization to provide new structured spectral element methods for high-order problems. Besides, to increase the flexibility, a C1-conforming rectangular spectral method in analogy to Argyris or Bell triangular elements are proposed for fourth-order equations, which serves as a preparative work towards conforming quadrilateral spectral elements for high-order equations.
Year
DOI
Venue
2019
10.1016/j.cam.2018.08.038
Journal of Computational and Applied Mathematics
Keywords
Field
DocType
65M70,65L60,41A10,41A30
Space time,Diagonal,Applied mathematics,Mathematical analysis,Constant coefficients,Matrix decomposition,Spacetime,Quadrilateral,Spectral method,Basis function,Mathematics
Journal
Volume
ISSN
Citations 
351
0377-0427
0
PageRank 
References 
Authors
0.34
11
3
Name
Order
Citations
PageRank
Chao Zhang1939103.66
Hanfeng Yao200.34
Huiyuan Li3346.21