Unconditionally energy stable second-order numerical scheme for the Allen–Cahn equation with a high-order polynomial free energy

Junseok Kim, Hyun Geun Lee

Research output: Contribution to journalArticlepeer-review

Abstract

In this article, we consider a temporally second-order unconditionally energy stable computational method for the Allen–Cahn (AC) equation with a high-order polynomial free energy potential. By modifying the nonlinear parts in the governing equation, we have a linear convex splitting scheme of the energy for the high-order AC equation. In addition, by combining the linear convex splitting with a strong-stability-preserving implicit–explicit Runge–Kutta (RK) method, the proposed method is linear, temporally second-order accurate, and unconditionally energy stable. Computational tests are performed to demonstrate that the proposed method is accurate, efficient, and energy stable.

Original languageEnglish
Article number416
JournalAdvances in Difference Equations
Volume2021
Issue number1
DOIs
Publication statusPublished - 2021 Dec

Keywords

  • Allen–Cahn equation
  • High-order polynomial free energy
  • Implicit–explicit RK scheme
  • Linear convex splitting

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

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