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Status已发表Published
TitleA Decreasing Upper Bound of the Energy for Time-Fractional Phase-Field Equations
Creator
Date Issued2023-04-01
Source PublicationCommunications in Computational Physics
ISSN1815-2406
Volume33Issue:4Pages:962-991
Abstract

In this article, we study the energy dissipation property of time-fractional Allen-Cahn equation. On the continuous level, we propose an upper bound of energy that decreases with respect to time and coincides with the original energy at t=0 and as t tends to ∞. This upper bound can also be viewed as a nonlocal-in-time modified energy which is the summation of the original energy and an accumulation term due to the memory effect of time-fractional derivative. In particular, the decrease of the modified energy indicates that the original energy indeed decays w.r.t. time in a small neighborhood at t=0. We illustrate the theory mainly with the time-fractional Allen- Cahn equation but it could also be applied to other time-fractional phase-field models such as the Cahn-Hilliard equation. On the discrete level, the decreasing upper bound of energy is useful for proving energy dissipation of numerical schemes. First-order L1 and second-order L2 schemes for the time-fractional Allen-Cahn equation have similar decreasing modified energies, so that stability can be established. Some numerical results are provided to illustrate the behavior of this modified energy and to verify our theoretical results.

Keywordenergy dissipation L1 approximation L2 approximation Time-fractional Allen-Cahn equation
DOI10.4208/cicp.OA-2022-0148
URLView source
Indexed BySCIE
Language英语English
WOS Research AreaPhysics
WOS SubjectPhysics, Mathematical
WOS IDWOS:000993886300002
Scopus ID2-s2.0-85161279707
Citation statistics
Cited Times:12[WOS]   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
Identifierhttp://repository.uic.edu.cn/handle/39GCC9TT/10562
CollectionFaculty of Science and Technology
Corresponding AuthorWang, Boyi
Affiliation
1.International Center for Mathematics,Southern University of Science and Technology,Shenzhen,518055,China
2.Division of Science and Technology,BNU-HKBU United International College,Zhuhai,519087,China
3.Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science,BNU-HKBU United International College,Zhuhai,519087,China
4.Department of Mathematics,Southern University of Science and Technology,Shenzhen,Guangdong,518055,China
5.Department of Mathematics,National University of Singapore,Singapore,119076,Singapore
6.Guangdong Provincial Key Laboratory of Computational Science and Material Design,Southern University of Science and Technology,Shenzhen,518055,China
Recommended Citation
GB/T 7714
Quan, Chaoyu,Tang, Tao,Wang, Boyiet al. A Decreasing Upper Bound of the Energy for Time-Fractional Phase-Field Equations[J]. Communications in Computational Physics, 2023, 33(4): 962-991.
APA Quan, Chaoyu, Tang, Tao, Wang, Boyi, & Yang, Jiang. (2023). A Decreasing Upper Bound of the Energy for Time-Fractional Phase-Field Equations. Communications in Computational Physics, 33(4), 962-991.
MLA Quan, Chaoyu,et al."A Decreasing Upper Bound of the Energy for Time-Fractional Phase-Field Equations". Communications in Computational Physics 33.4(2023): 962-991.
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