A fourth-order spatial accurate and practically stable compact scheme for the Cahn-Hilliard equation

Chaeyoung Lee, Darae Jeong, Jaemin Shin, Yibao Li, Junseok Kim

Research output: Contribution to journalArticle

13 Citations (Scopus)


We present a fourth-order spatial accurate and practically stable compact difference scheme for the Cahn-Hilliard equation. The compact scheme is derived by combining a compact nine-point formula and linearly stabilized splitting scheme. The resulting system of discrete equations is solved by a multigrid method. Numerical experiments are conducted to verify the practical stability and fourth-order accuracy of the proposed scheme. We also demonstrate that the compact scheme is more robust and efficient than the non-compact fourth-order scheme by applying to parallel computing and adaptive mesh refinement.

Original languageEnglish
Pages (from-to)17-28
Number of pages12
JournalPhysica A: Statistical Mechanics and its Applications
Publication statusPublished - 2014 Sep 1



  • Adaptive mesh refinement
  • Cahn-Hilliard equation
  • Fourth-order compact scheme
  • Multigrid
  • Parallel computing
  • Practically stable scheme

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistics and Probability

Cite this