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Stabilized Crank-Nicolson/Adams-Bashforth Schemes for Phase Field Models

Published online by Cambridge University Press:  28 May 2015

Xinlong Feng ,
Tao Tang  and
Jiang Yang
Xinlong Feng*
Affiliation:
Department of Mathematics & Institute for Computational and Theoretical Studies, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China
Tao Tang*
Affiliation:
Department of Mathematics & Institute for Computational and Theoretical Studies, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China
Jiang Yang*
Affiliation:
Department of Mathematics & Institute for Computational and Theoretical Studies, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China
*
Corresponding author. Email: fxlmath@gmail.com
Corresponding author. Email: ttang@math.hkbu.edu.hk
Corresponding author. Email: jiangy@hkbu.edu.hk
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Abstract

In this paper, stabilized Crank-Nicolson/Adams-Bashforth schemes are presented for the Allen-Cahn and Cahn-Hilliard equations. It is shown that the proposed time discretization schemes are either unconditionally energy stable, or conditionally energy stable under some reasonable stability conditions. Optimal error estimates for the semi-discrete schemes and fully-discrete schemes will be derived. Numerical experiments are carried out to demonstrate the theoretical results.

Keywords

35L7065N3076D06Allen-Cahn equationCahn-Hilliard equationCrank-Nicolson schemeAdams-Bashforth schemeimplicit-explicit methoderror estimates
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 3 , Issue 1 , February 2013 , pp. 59 - 80
Copyright
Copyright © Global-Science Press 2013

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