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

Stabilized Crank-Nicolson/Adams-Bashforth Schemes for Phase Field Models
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Year:    2013

East Asian Journal on Applied Mathematics, Vol. 3 (2013), Iss. 1 : pp. 59–80

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.200113.220213a

East Asian Journal on Applied Mathematics, Vol. 3 (2013), Iss. 1 : pp. 59–80

Published online:    2013-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:    Allen-Cahn equation Cahn-Hilliard equation Crank-Nicolson scheme Adams-Bashforth scheme implicit-explicit method error estimates.

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