Energy-Decaying Extrapolated RK--SAV Methods for the Allen--Cahn and Cahn--Hilliard Equations
Abstract
We construct and analyze a class of extrapolated and linearized Runge--Kutta (RK) methods, which can be of arbitrarily high order, for the time discretization of the Allen--Cahn and Cahn--Hilliard phase field equations, based on the scalar auxiliary variable (SAV) formulation. We prove that the proposed $q$-stage RK--SAV methods have $q$th-order convergence in time and satisfy a discrete version of the energy decay property. Numerical examples are provided to illustrate the discrete energy decay property and accuracy of the proposed methods.
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Information
Published In
SIAM Journal on Scientific Computing
Pages: A3703 - A3727
DOI: 10.1137/19M1264412
ISSN (online): 1095-7197
Copyright
© 2019, Society for Industrial and Applied Mathematics.
History
Submitted: 28 May 2019
Accepted: 23 September 2019
Published online: 21 November 2019
Keywords
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Funding Information
National Natural Science Foundation of China https://doi.org/10.13039/501100001809 : 11771162
Research Grants Council, University Grants Committee https://doi.org/10.13039/501100002920 : 15300519
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