A hybrid FEM for solving the Allen-Cahn equation

Jaemin Shin, Seong Kwan Park, Junseok Kim

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


We present an unconditionally stable hybrid finite element method for solving the Allen-Cahn equation, which describes the temporal evolution of a non-conserved phase-field during the antiphase domain coarsening in a binary mixture. Its various modified forms have been applied to image analysis, motion by mean curvature, crystal growth, topology optimization, and two-phase fluid flows. The hybrid method is based on the operator splitting method. The equation is split into a heat equation and a nonlinear equation. An implicit finite element method is applied to solve the diffusion equation and then the nonlinear equation is solved analytically. Various numerical experiments are presented to confirm the accuracy and efficiency of the method. Our simulation results are consistent with previous theoretical and numerical results.

Original languageEnglish
Pages (from-to)606-612
Number of pages7
JournalApplied Mathematics and Computation
Publication statusPublished - 2014 Oct 1

Bibliographical note

Funding Information:
The author (J. Shin) is supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2009-0093827). The corresponding author (J.S. Kim) was supported by a Korea University Grant. The authors also wish to thank the reviewers for the constructive and helpful comments on the revision of this article.


  • Allen-Cahn equation
  • Finite element method
  • Operator splitting method
  • Unconditionally stable scheme

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


Dive into the research topics of 'A hybrid FEM for solving the Allen-Cahn equation'. Together they form a unique fingerprint.

Cite this