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.
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