Junseok Kim, Kyungkeun Kang, John Lowengrub

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)


We develop a conservative, second order accurate fully implicit discretization of ternary (three-phase) Cahn-Hilliard (CH) systems that has an associated discrete energy functional. This is an extension of our work for two-phase systems [13]. We analyze and prove convergence of the scheme. To efficiently solve the discrete system at the implicit time-level, we use a nonlinear multigrid method. The resulting scheme is efficient, robust and there is at most a 1st order time step constraint for stability. We demonstrate convergence of our scheme numerically and we present several simulations of phase transitions in ternary systems.

Original languageEnglish
Pages (from-to)53-77
Number of pages25
JournalCommunications in Mathematical Sciences
Issue number1
Publication statusPublished - 2004

Bibliographical note

Funding Information:
Appendix D. The first (J.S. Kim) and third (J. S. Lowengrub) authors acknowledge the support of the Department of Energy, Office of Basic Energy Sciences and the National Science Foundation. The authors are also grateful for the support of the Minnesota Supercomputer Institute, the Network & Academic Computing Services (NACS) at UCI, and the hospitality of the Institute for Mathematics and its Applications.

Publisher Copyright:
© 2004 International Press

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics


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