Characterizing the stabilization size for semi-implicit fourier-spectral method to phase field equations

Dong Li, Zhonghua QIAO, Tao TANG

Research output: Contribution to journalArticlepeer-review

54 Citations (Scopus)

Abstract

Recent results in the literature provide computational evidence that the stabilized semi-implicit time-stepping method can eficiently simulate phase field problems involving fourth order nonlinear diffusion, with typical examples like the Cahn-Hilliard equation and the thin film type equation. The up-to-date theoretical explanation of the numerical stability relies on the assumption that the derivative of the nonlinear potential function satisfies a Lipschitz-type condition, which in a rigorous sense, implies the boundedness of the numerical solution. In this work we remove the Lipschitz assumption on the nonlinearity and prove unconditional energy stability for the stabilized semi-implicit time-stepping methods. It is shown that the size of the stabilization term depends on the initial energy and the perturbation parameter but is independent of the time step. The corresponding error analysis is also established under minimal nonlinearity and regularity assumptions.

Original languageEnglish
Pages (from-to)1653-1681
Number of pages29
JournalSIAM Journal on Numerical Analysis
Volume54
Issue number3
DOIs
Publication statusPublished - 2016

Scopus Subject Areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Cahn-Hilliard
  • Energy stable
  • Epitaxy
  • Large time stepping
  • Thin film

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