On large time-stepping methods for the Cahn-Hilliard equation

Yinnian He; Yunxian Liu; Tao TANG

doi:10.1016/j.apnum.2006.07.026

On large time-stepping methods for the Cahn-Hilliard equation

Yinnian He, Yunxian Liu, Tao TANG^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

192 Citations (Scopus)

Abstract

In this work, we will analyze a class of large time-stepping methods for the Cahn-Hilliard equation. The equation is discretized by Fourier spectral method in space and semi-implicit schemes in time. For first-order semi-implicit scheme, the stability and convergence properties are investigated based on an energy approach. Here stability means that the decay of energy is preserved. The numerical experiments are used to demonstrate the effectiveness of the large time-stepping approaches.

Original language	English
Pages (from-to)	616-628
Number of pages	13
Journal	Applied Numerical Mathematics
Volume	57
Issue number	5-7 SPEC. ISS.
DOIs	https://doi.org/10.1016/j.apnum.2006.07.026
Publication status	Published - May 2007

Scopus Subject Areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

User-Defined Keywords

Cahn-Hilliard equation
Decay of energy
Large time-stepping method
Semi-implicit scheme
Spectral method
Stability

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10.1016/j.apnum.2006.07.026

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title = "On large time-stepping methods for the Cahn-Hilliard equation",

abstract = "In this work, we will analyze a class of large time-stepping methods for the Cahn-Hilliard equation. The equation is discretized by Fourier spectral method in space and semi-implicit schemes in time. For first-order semi-implicit scheme, the stability and convergence properties are investigated based on an energy approach. Here stability means that the decay of energy is preserved. The numerical experiments are used to demonstrate the effectiveness of the large time-stepping approaches.",

keywords = "Cahn-Hilliard equation, Decay of energy, Large time-stepping method, Semi-implicit scheme, Spectral method, Stability",

author = "Yinnian He and Yunxian Liu and Tao TANG",

note = "Funding Information: The research of Y. He was supported in part by National Science Foundation of China Grant #10371095. The research of Y. Liu was supported in part by National Science Foundation of China Grant #10501031. This project was supported by CERG Grants of Hong Kong Research Grant Council, FRG grants of Hong Kong Baptist University, and NSAF Grant #10476032 of National Science Foundation of China.",

year = "2007",

month = may,

doi = "10.1016/j.apnum.2006.07.026",

language = "English",

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pages = "616--628",

journal = "Applied Numerical Mathematics",

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T1 - On large time-stepping methods for the Cahn-Hilliard equation

AU - He, Yinnian

AU - Liu, Yunxian

AU - TANG, Tao

N1 - Funding Information: The research of Y. He was supported in part by National Science Foundation of China Grant #10371095. The research of Y. Liu was supported in part by National Science Foundation of China Grant #10501031. This project was supported by CERG Grants of Hong Kong Research Grant Council, FRG grants of Hong Kong Baptist University, and NSAF Grant #10476032 of National Science Foundation of China.

PY - 2007/5

Y1 - 2007/5

N2 - In this work, we will analyze a class of large time-stepping methods for the Cahn-Hilliard equation. The equation is discretized by Fourier spectral method in space and semi-implicit schemes in time. For first-order semi-implicit scheme, the stability and convergence properties are investigated based on an energy approach. Here stability means that the decay of energy is preserved. The numerical experiments are used to demonstrate the effectiveness of the large time-stepping approaches.

AB - In this work, we will analyze a class of large time-stepping methods for the Cahn-Hilliard equation. The equation is discretized by Fourier spectral method in space and semi-implicit schemes in time. For first-order semi-implicit scheme, the stability and convergence properties are investigated based on an energy approach. Here stability means that the decay of energy is preserved. The numerical experiments are used to demonstrate the effectiveness of the large time-stepping approaches.

KW - Cahn-Hilliard equation

KW - Decay of energy

KW - Large time-stepping method

KW - Semi-implicit scheme

KW - Spectral method

KW - Stability

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DO - 10.1016/j.apnum.2006.07.026

M3 - Journal article

AN - SCOPUS:34147135231

SN - 0168-9274

VL - 57

SP - 616

EP - 628

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

IS - 5-7 SPEC. ISS.

ER -

On large time-stepping methods for the Cahn-Hilliard equation

Abstract

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