Numerical Methods for Partial Differential Equations

RESEARCH ARTICLE

Energy stability and convergence of the scalar auxiliary variable Fourier-spectral method for the viscous Cahn–Hilliard equation

Nan Zheng

School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing, Xiamen University, Xiamen, China

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Xiaoli Li,

Corresponding Author

Xiaoli Li

[email protected]

orcid.org/0000-0001-9245-0647

School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing, Xiamen University, Xiamen, China

Correspondence

Xiaoli Li, School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing, Xiamen University, Xiamen, Fujian 361005, China.

Email: [email protected]

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Nan Zheng,

Nan Zheng

School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing, Xiamen University, Xiamen, China

Search for more papers by this author

Xiaoli Li,

Corresponding Author

Xiaoli Li

[email protected]

orcid.org/0000-0001-9245-0647

School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing, Xiamen University, Xiamen, China

Correspondence

Xiaoli Li, School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing, Xiamen University, Xiamen, Fujian 361005, China.

Email: [email protected]

Search for more papers by this author

First published: 07 January 2020

https://doi.org/10.1002/num.22461

Citations: 3

Funding information Postdoctoral Science Foundation of China, 2019M650152; BX20190187; National Natural Science Foundation of China, 11901489

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Abstract

In this paper, we develop two linear and unconditionally energy stable Fourier-spectral schemes for solving viscous Cahn–Hilliard equation based on the recently scalar auxiliary variable approach. The temporal discretizations are built upon the first-order Euler method and second-order Crank–Nicolson method, respectively. We carry out the energy stability and error analysis rigorously. Various classical numerical experiments are performed to validate the efficiency and accuracy of the proposed schemes.

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Volume36, Issue5

September 2020

Pages 998-1011

Energy stability and convergence of the scalar auxiliary variable Fourier-spectral method for the viscous Cahn–Hilliard equation

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Energy stability and convergence of the scalar auxiliary variable Fourier-spectral method for the viscous Cahn–Hilliard equation

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