Arbitrarily High Order and Fully Discrete Extrapolated RK–SAV/DG Schemes for Phase-field Gradient Flows

Tao Tang, Xu Wu*, Jiang Yang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

3 Citations (Scopus)


In this paper, we construct and analyze a fully discrete method for phase-field gradient flows, which uses extrapolated Runge–Kutta with scalar auxiliary variable (RK–SAV) method in time and discontinuous Galerkin (DG) method in space. We propose a novel technique to decouple the system, after which only several elliptic scalar problems with constant coefficients need to be solved independently. Discrete energy decay property of the method is proved for gradient flows. The scheme can be of arbitrarily high order both in time and space, which is demonstrated rigorously for the Allen–Cahn equation and the Cahn–Hilliard equation. More precisely, optimal L2-error bound in space and qth-order convergence rate in time are obtained for q-stage extrapolated RK–SAV/DG method. Several numerical experiments are carried out to verify the theoretical results.

Original languageEnglish
Article number38
Number of pages23
JournalJournal of Scientific Computing
Issue number2
Early online date16 Sept 2022
Publication statusPublished - Nov 2022

Scopus Subject Areas

  • Theoretical Computer Science
  • Software
  • Numerical Analysis
  • Engineering(all)
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Allen–Cahn equation
  • Cahn–Hilliard equation
  • Convergence and error analysis
  • Energy stability
  • Gradient flows
  • Phase-field models


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