Convergence Analysis of Exponential Time Differencing Schemes for the Cahn-Hilliard Equation

Xiao Li, Lili Ju, Xucheng Meng

Research output: Journal article publicationJournal articleAcademic researchpeer-review

21 Citations (Scopus)

Abstract

In this paper, we rigorously prove the convergence of fully discrete firstand second-order exponential time differencing schemes for solving the Cahn-Hilliard equation. Our analysesmainly followthe standard procedurewith the consistency and stability estimates for numerical error functions, while the technique of higher-order consistency analysis is adopted in order to obtain the uniform L boundedness of the numerical solutions under some moderate constraints on the time step and spatial mesh sizes. This paper provides a theoretical support for numerical analysis of exponential time differencing and other related numerical methods for phase field models, in which an assumption on the uniform L boundedness is usually needed.

Original languageEnglish
Pages (from-to)1510-1529
Number of pages20
JournalCommunications in Computational Physics
Volume26
Issue number5
DOIs
Publication statusPublished - 2019

Keywords

  • Cahn-Hilliard equation
  • Convergence analysis
  • Exponential time differencing
  • Uniform L boundedness

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

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