On Second Order Semi-implicit Fourier Spectral Methods for 2D Cahn–Hilliard Equations

Dong Li, Zhonghua Qiao

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81 Citations (Scopus)


We consider several seconder order in time stabilized semi-implicit Fourier spectral schemes for 2D Cahn–Hilliard equations. We introduce new stabilization techniques and prove unconditional energy stability for modified energy functionals. We also carry out a comparative study of several classical stabilization schemes and identify the corresponding stability regions. In several cases the energy stability is proved under relaxed constraints on the size of the time steps. We do not impose any Lipschitz assumption on the nonlinearity. The error analysis is obtained under almost optimal regularity assumptions.
Original languageEnglish
Pages (from-to)301-341
Number of pages41
JournalJournal of Scientific Computing
Issue number1
Publication statusPublished - 1 Jan 2017


  • Cahn–Hilliard
  • Energy stable
  • Large time stepping
  • Second order
  • Semi-implicit

ASJC Scopus subject areas

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

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