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Parameter-Free Time Adaptivity Based on Energy Evolution for the Cahn-Hilliard Equation

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Miscellaneous topics - Partial differential equations Elliptic equations and systems Partial differential equations, boundary value problems Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  17 May 2016

Fuesheng Luo ,
Tao Tang  and
Hehu Xie
Fuesheng Luo*
Affiliation:
The Third Institute of Oceanography, SOA, Xiamen 361005, China
Tao Tang*
Affiliation:
Department of Mathematics, Southern University of Science and Technology of China, Shenzhen, Guangdong 518055, China Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
Hehu Xie*
Affiliation:
LSEC, ICMSEC, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
*
*Corresponding author. Email addresses:luofusheng@tio.org.cn (F. Luo), tangt@sustc.edu.cn (T. Tang), hhxie@lsec.cc.ac.cn (H. Xie)
*Corresponding author. Email addresses:luofusheng@tio.org.cn (F. Luo), tangt@sustc.edu.cn (T. Tang), hhxie@lsec.cc.ac.cn (H. Xie)
*Corresponding author. Email addresses:luofusheng@tio.org.cn (F. Luo), tangt@sustc.edu.cn (T. Tang), hhxie@lsec.cc.ac.cn (H. Xie)
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Abstract

It is known that large time-stepping method are useful for simulating phase field models. In this work, an adaptive time-stepping strategy is proposed based on numerical energy stability and equi-distribution principle. The main idea is to use the energy variation as an indicator to update the time step, so that the resulting algorithm is free of user-defined parameters, which is different from several existing approaches. Some numerical experiments are presented to illustrate the effectiveness of the algorithms.

Keywords

Adaptive time-stepping methodCahn-Hilliard equationCrank-Nicolson schemeconvex splitting method

MSC classification

Secondary: 65N15: Error bounds 35J25: Boundary value problems for second-order elliptic equations 35Q99: None of the above, but in this section 35R99: None of the above, but in this section 65M12: Stability and convergence of numerical methods 65M70: Spectral, collocation and related methods
Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 5 , May 2016 , pp. 1542 - 1563
Copyright
Copyright © Global-Science Press 2016 

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