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Energy stability and convergence of the scalar auxiliary variable Fourier‐spectral method for the viscous Cahn–Hilliard equation
Author(s) -
Zheng Nan,
Li Xiaoli
Publication year - 2020
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22461
Subject(s) - mathematics , cahn–hilliard equation , scalar (mathematics) , convergence (economics) , fourier transform , stability (learning theory) , euler's formula , energy method , spectral method , backward euler method , energy (signal processing) , variable (mathematics) , mathematical analysis , euler equations , partial differential equation , computer science , statistics , geometry , machine learning , economics , economic growth
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.