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Implicit-Explicit Scheme for the Allen-Cahn Equation Preserves the Maximum Principle

Implicit-Explicit Scheme for the Allen-Cahn Equation Preserves the Maximum Principle
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Year:    2016

Author:    Tao Tang, Jiang Yang

Journal of Computational Mathematics, Vol. 34 (2016), Iss. 5 : pp. 451–461

Abstract

It is known that the Allen-Chan equations satisfy the maximum principle. Is this true for numerical schemes? To the best of our knowledge, the state-of-art stability framework is the nonlinear energy stability which has been studied extensively for the phase field type equations. In this work, we will show that a stronger stability under the infinity norm can be established for the implicit-explicit discretization in time and central finite difference in space. In other words, this commonly used numerical method for the Allen-Cahn equation preserves the maximum principle.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1603-m2014-0017

Journal of Computational Mathematics, Vol. 34 (2016), Iss. 5 : pp. 451–461

Published online:    2016-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    11

Keywords:    Allen-Cahn Equations Implicit-explicit scheme Maximum principle Nonlinear energy stability.

Author Details

Tao Tang

Jiang Yang

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