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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

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Online
ISSN
1609-9389
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Volume 14, Issue 3 (Jul 2014)

Issues

The Tailored Finite Point Method

Houde Han
  • Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P. R. China
  • Email:
/ Zhongyi Huang
  • Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P. R. China
  • Email:
Published Online: 2014-04-26 | DOI: https://doi.org/10.1515/cmam-2014-0012

Abstract.

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.

Keywords: Tailored Finite Point Method; Singular Perturbation Problem; Boundary/Interior Layer; Discrete Maximum Principle; High Frequency Waves; Discrete-Ordinate Transport Equation; Multiscale Elliptic Problem

MSC: 65N35; 65N12

About the article

Received: 2014-02-28

Revised: 2014-03-28

Accepted: 2014-04-04

Published Online: 2014-04-26

Published in Print: 2014-07-01


Funding Source: NSFC

Award identifier / Grant number: 11322113, 11371218, 91330203

Funding Source: National Basic Research Program of China

Award identifier / Grant number: 2011CB309705


Citation Information: Computational Methods in Applied Mathematics, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2014-0012. Export Citation

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