Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 41, Issue 6, Pages A3703-A3727Publisher
SIAM PUBLICATIONS
DOI: 10.1137/19M1264412
Keywords
Allen-Cahn equation; Cahn-Hilliard equation; energy decay; scalar auxiliary variable; Runge-Kutta methods; extrapolation; Gauss methods; Radau IIA methods; algebraic stability
Categories
Funding
- Hong Kong RGC [15300519]
- NSFC [11771162]
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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 qth-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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