On energy stable, maximum-principle preserving, second-order bdf scheme with variable steps for the allen-cahn equation

HONG LIN LIAO, TAO TANG, TAO ZHOU

Research output: Contribution to journalJournal articlepeer-review

53 Citations (Scopus)

Abstract

In this work, we investigate the two-step backward differentiation formula (BDF2) with nonuniform grids for the Allen-Cahn equation. We show that the nonuniform BDF2 scheme is energy stable under the time-step ratio restriction rk := τ k/τ k 1 < (3 + 17)/2 3.561. Moreover, by developing a novel kernel recombination and complementary technique, we show, for the first time, the discrete maximum bound principle of the BDF2 scheme under the time-step ratio restriction rk < 1 + 2 2.414 and a practical time-step constraint. The second-order rate of convergence in the maximum norm is also presented. Numerical experiments are provided to support the theoretical findings.

Original languageEnglish
Pages (from-to)2294-2314
Number of pages21
JournalSIAM Journal on Numerical Analysis
Volume58
Issue number4
DOIs
Publication statusPublished - 2020

Scopus Subject Areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Allen-Cahn equation
  • Convergence analysis
  • Discrete maximum principle
  • Energy stability
  • Nonuniform BDF2 scheme

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