A stable second-order BDF scheme for the three-dimensional Cahn–Hilliard–Hele–Shaw system

Yibao Li, Qian Yu, Weiwei Fang, Binhu Xia, Junseok Kim

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


We propose a stable scheme to solve numerically the Cahn–Hilliard–Hele–Shaw system in three-dimensional space. In the proposed scheme, we discretize the space and time derivative terms by combining with backward differentiation formula, which turns out to be both second-order accurate in space and time. Using this method, a set of linear elliptic equations are solved instead of the complicated and high-order nonlinear equations. We prove that our proposed scheme is uniquely solvable. We use a linear multigrid solver, which is fast and convergent, to solve the resulting discrete system. The numerical tests indicate that our scheme can use a large time step. The accuracy and other capability of the proposed algorithm are demonstrated by various computational results.

Original languageEnglish
Article number3
JournalAdvances in Computational Mathematics
Issue number1
Publication statusPublished - 2021 Feb


  • Backward differentiation formula
  • Cahn–Hilliard–Hele–Shaw
  • Linear multigrid
  • Second-order accuracy
  • Unique solvability

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


Dive into the research topics of 'A stable second-order BDF scheme for the three-dimensional Cahn–Hilliard–Hele–Shaw system'. Together they form a unique fingerprint.

Cite this