A second-order decoupled energy stable numerical scheme for Cahn-Hilliard-Hele-Shaw system

Yali Gao, Rui Li, Liquan Mei, Yanping Lin

Research output: Journal article publicationJournal articleAcademic researchpeer-review

15 Citations (Scopus)


In this paper, we develop a novel second order in time, decoupled, energy stable finite element scheme for simulation of Cahn-Hilliard-Hele-Shaw system. The idea of scalar auxiliary variable approach is introduced to handle the nonlinear bulk. An operator-splitting strategy is utilized to fully decouple the coupled Cahn-Hilliard equation and Darcy equation. A full discretization is built in the framework of Galerkin finite element method. The unique solvability of numerical solution and preservation of energy law are rigorously established. Numerical experiences are recorded to illustrate the features of the designed numerical method, verify the theoretical results and conduct realistic applications.

Original languageEnglish
Pages (from-to)338-355
Number of pages18
JournalApplied Numerical Mathematics
Publication statusPublished - Nov 2020


  • Cahn-Hilliard-Hele-Shaw system
  • Energy stability
  • Finite element method
  • Scalar auxiliary variable approach
  • Second order in time

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics


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