Stabilized Crank-Nicolson/Adams-Bashforth schemes for phase field models

Xinlong Feng, Tao TANG*, Jiang Yang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

49 Citations (Scopus)

Abstract

In this paper, stabilized Crank-Nicolson/Adams-Bashforth schemes are presented for the Allen-Cahn and Cahn-Hilliard equations. It is shown that the proposed time discretization schemes are either unconditionally energy stable, or conditionally energy stable under some reasonable stability conditions. Optimal error estimates for the semi-discrete schemes and fully-discrete schemes will be derived. Numerical experiments are carried out to demonstrate the theoretical results.

Original languageEnglish
Pages (from-to)59-80
Number of pages22
JournalEast Asian Journal on Applied Mathematics
Volume3
Issue number1
DOIs
Publication statusPublished - Feb 2013

Scopus Subject Areas

  • Applied Mathematics

User-Defined Keywords

  • Adams-Bashforth scheme
  • Allen-Cahn equation
  • Cahn-Hilliard equation
  • Crank-Nicolson scheme
  • Error estimates
  • Implicit-explicit method

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