On Symmetry Breaking of Allen-Cahn

Dong Li, Chaoyu Quan*, Tao Tang, Wen Yang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

2 Citations (Scopus)


This paper is concerned with numerical solutions for the Allen-Cahn equation with standard double well potential and periodic boundary conditions. Surprisingly it is found that using standard numerical discretizations with high precision computational solutions may converge to completely incorrect steady states. This happens for very smooth initial data and state-of-the-art algorithms. We analyze this phenomenon and showcase the resolution of this problem by a new symmetry-preserving filter technique. We develop a new theoretical framework and rigorously prove the convergence to steady states for the filtered solutions.

Original languageEnglish
Pages (from-to)221-243
Number of pages23
JournalCSIAM Transactions on Applied Mathematics
Issue number2
Publication statusPublished - Jun 2022

Scopus Subject Areas

  • Applied Mathematics

User-Defined Keywords

  • Allen-Cahn equation
  • steady state
  • symmetry breaking


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