STABILITY AND CONVERGENCE ANALYSIS FOR THE IMPLICIT-EXPLICIT METHOD TO THE CAHN-HILLIARD EQUATION

Dong Li*, Chaoyu Quan, Tao Tang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

8 Citations (Scopus)

Abstract

Implicit-explicit methods have been successfully used for the efficient numerical simulation of phase field problems such as the Cahn-Hilliard equation or thin film type equations. Due to the lack of maximum principle and stiffness caused by the effect of small dissipation coefficient, most existing theoretical analysis relies on adding additional stabilization terms, mollifying the nonlinearity or introducing auxiliary variables which implicitly either changes the structure of the problem or trades accuracy for stability in a subtle way. In this work, we introduce a robust theoretical framework to analyze directly the stability and accuracy of the standard implicit-explicit approach without stabilization or any other modification. We take the Cahn-Hilliard equation as a model case and provide a rigorous stability and convergence analysis for the original semi-discrete scheme under certain time step constraints. These settle several questions which have been open since the work of Chen and Shen [Comput. Phys. Comm. 108 (1998), pp. 147–158].
Original languageEnglish
Pages (from-to)785-809
Number of pages25
JournalMathematics of Computation
Volume91
Issue number334
DOIs
Publication statusPublished - Mar 2022

Scopus Subject Areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Cahn-hilliard equation
  • Implicit-explicit method

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