Tailored Finite Point Method for Parabolic Problems

In this paper, we propose a class of new tailored finite point methods (TFPM) for the numerical solution of parabolic equations. Our finite point method has been tailored based on the local exponential basis functions. By the idea of our TFPM, we can recover all the traditional finite difference sch...

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Bibliographic Details
Published inJournal of computational methods in applied mathematics Vol. 16; no. 4; pp. 543 - 562
Main Authors Huang, Zhongyi, Yang, Yi
Format Journal Article
LanguageEnglish
Published Minsk De Gruyter 01.10.2016
Walter de Gruyter GmbH
Subjects
65M70
65M80
80A20
Convection-diffusion equation
Parabolic Equation
Shishkin Meshes, Uniform Convergence
Singular Perturbation
Tailored Finite Point Method
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ISSN1609-4840
1609-9389
DOI10.1515/cmam-2016-0017

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Summary:In this paper, we propose a class of new tailored finite point methods (TFPM) for the numerical solution of parabolic equations. Our finite point method has been tailored based on the local exponential basis functions. By the idea of our TFPM, we can recover all the traditional finite difference schemes. We can also construct some new TFPM schemes with better stability condition and accuracy. Furthermore, combining with the Shishkin mesh technique, we construct the uniformly convergent TFPM scheme for the convection-dominant convection-diffusion problem. Our numerical examples show the efficiency and reliability of TFPM.
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ISSN:1609-4840
1609-9389
DOI:10.1515/cmam-2016-0017