First and second order numerical methods based on a new convex splitting for phase-field crystal equation

Jaemin Shin, Hyun Geun Lee, June Yub Lee

Research output: Contribution to journalArticlepeer-review

49 Scopus citations

Abstract

The phase-field crystal equation derived from the Swift–Hohenberg energy functional is a sixth order nonlinear equation. We propose numerical methods based on a new convex splitting for the phase-field crystal equation. The first order convex splitting method based on the proposed splitting is unconditionally gradient stable, which means that the discrete energy is non-increasing for any time step. The second order scheme is unconditionally weakly energy stable, which means that the discrete energy is bounded by its initial value for any time step. We prove mass conservation, unique solvability, energy stability, and the order of truncation error for the proposed methods. Numerical experiments are presented to show the accuracy and stability of the proposed splitting methods compared to the existing other splitting methods. Numerical tests indicate that the proposed convex splitting is a good choice for numerical methods of the phase-field crystal equation.

Original languageEnglish
Pages (from-to)519-542
Number of pages24
JournalJournal of Computational Physics
Volume327
DOIs
StatePublished - 15 Dec 2016

Keywords

  • Convex splitting method
  • Energy stability
  • Gradient stability
  • Phase-field crystal equation
  • Swift–Hohenberg functional

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