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Tailored finite point method based on exponential bases for convection-diffusion-reaction equation


Authors: Houde Han and Zhongyi Huang
Journal: Math. Comp. 82 (2013), 213-226
MSC (2010): Primary 65-xx; Secondary 35-xx
DOI: https://doi.org/10.1090/S0025-5718-2012-02616-0
Published electronically: June 6, 2012
MathSciNet review: 2983022
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Abstract: In this paper, we propose a class of new tailored finite point methods (TFPM) for the numerical solution of a type of convection-diffusion-reaction problems in two dimensions. Our finite point method has been tailored based on the local exponential basis functions. Furthermore, our TFPM satisfies the discrete maximum principle automatically. We also study the error estimates of our TFPM. We prove that our TFPM can achieve good accuracy even when the mesh size $ h\gg \varepsilon $ for some cases without any prior knowledge of the boundary layers. Our numerical examples show the efficiency and reliability of our method.


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Additional Information

Houde Han
Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
Email: hhan@math.tsinghua.edu.cn

Zhongyi Huang
Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
Email: zhuang@math.tsinghua.edu.cn

DOI: https://doi.org/10.1090/S0025-5718-2012-02616-0
Keywords: Tailored finite point method, singular perturbation problem, boundary layer, discrete maximum principle
Received by editor(s): November 29, 2009
Received by editor(s) in revised form: May 2, 2010
Published electronically: June 6, 2012
Additional Notes: H. Han was supported by the NSFC Project No. 10971116.
Z. Huang was supported by the NSFC Project No. 11071139, the National Basic Research Program of China under the grant 2011CB309705, Tsinghua University Initiative Scientific Research Program.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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