期刊
COMPUTATIONAL METHODS IN APPLIED MATHEMATICS
卷 14, 期 3, 页码 321-345出版社
WALTER DE GRUYTER GMBH
DOI: 10.1515/cmam-2014-0012
关键词
Tailored Finite Point Method; Singular Perturbation Problem; Boundary/Interior Layer; Discrete Maximum Principle; High Frequency Waves; Discrete-Ordinate Transport Equation; Multiscale Elliptic Problem
资金
- NSFC [11371218, 91330203, 11322113]
- National Basic Research Program of China [2011CB309705]
In this paper, a brief review of tailored finite point methods (TFPM) is given. The TFPM is a new approach to construct the numerical solutions of partial differential equations. The TFPM has been tailored based on the local properties of the solution for each given problem. Especially, the TFPM is very efficient for solutions which are not smooth enough, e.g., for solutions possessing boundary/interior layers or solutions being highly oscillated. Recently, the TFPM has been applied to singular perturbation problems, the Helmholtz equation with high wave numbers, the first-order wave equation in high frequency cases, transport equations with interface, second-order elliptic equations with rough or highly oscillatory coefficients, etc.
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