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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*
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.

Type
Research Article
Copyright
Copyright © Global-Science Press 2013

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