Energy-decaying extrapolated Rk–SAV methods for the Allen–Cahn and Cahn–Hilliard equations

Georgios Akrivis, Buyang Li, Dongfang Li

Research output: Journal article publicationJournal articleAcademic researchpeer-review

8 Citations (Scopus)

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 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.

Original languageEnglish
Pages (from-to)A3703-A3727
Number of pages24
JournalSIAM Journal on Scientific Computing
Volume41
Issue number6
DOIs
Publication statusPublished - 21 Nov 2019

Keywords

  • Algebraic stability
  • Allen–Cahn equation
  • Cahn–Hilliard equation
  • Energy decay
  • Extrapolation
  • Gauss methods
  • Radau IIA methods
  • Runge–Kutta methods
  • Scalar auxiliary variable

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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