The Tailored Finite Point Method

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...

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Bibliographic Details
Published inJournal of computational methods in applied mathematics Vol. 14; no. 3; pp. 321 - 345
Main Authors Han, Houde, Huang, Zhongyi
Format Journal Article
LanguageEnglish
Published De Gruyter 01.07.2014
Subjects
65N12
65N35
Boundary/Interior Layer
Discrete Maximum Principle
Discrete-Ordinate Transport Equation
High Frequency Waves
Multiscale Elliptic Problem
Singular Perturbation Problem
Tailored Finite Point Method
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ISSN1609-4840
1609-9389
1609-9389
DOI10.1515/cmam-2014-0012

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Summary: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.
ISSN:1609-4840
1609-9389
1609-9389
DOI:10.1515/cmam-2014-0012