Year: 2022
Author: Dong Li, Chaoyu Quan, Tao Tang, Wen Yang
CSIAM Transactions on Applied Mathematics, Vol. 3 (2022), Iss. 2 : pp. 221–243
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/csiam-am.SO-2021-0030
CSIAM Transactions on Applied Mathematics, Vol. 3 (2022), Iss. 2 : pp. 221–243
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Allen-Cahn equation symmetry breaking steady state.
Author Details
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https://doi.org/10.1016/j.jcp.2023.112058 [Citations: 0]