Please use this identifier to cite or link to this item:
http://hdl.handle.net/10397/95820
Title: | Stabilized exponential-SAV schemes preserving energy dissipation law and maximum bound principle for the Allen–Cahn type equations | Authors: | Ju, L Li, X Qiao, Z |
Issue Date: | Jul-2022 | Source: | Journal of scientific computing, 8 July 2022, v. 92, 66 | Abstract: | It is well-known that the Allen–Cahn equation not only satisfies the energy dissipation law but also possesses the maximum bound principle (MBP) in the sense that the absolute value of its solution is pointwise bounded for all time by some specific constant under appropriate initial/boundary conditions. In recent years, the scalar auxiliary variable (SAV) method and many of its variants have attracted much attention in numerical solutions for gradient flow problems due to their inherent advantage of preserving certain discrete analogues of the energy dissipation law. However, existing SAV schemes usually fail to preserve the MBP when applied to the Allen–Cahn equation. In this paper, we develop and analyze new first- and second-order stabilized exponential-SAV schemes for a class of Allen–Cahn type equations, which are shown to simultaneously preserve the energy dissipation law and MBP in discrete settings. In addition, optimal error estimates for the numerical solutions are rigorously obtained for both schemes. Extensive numerical tests and comparisons are also conducted to demonstrate the performance of the proposed schemes. | Keywords: | Maximum bound principle Energy dissipation Stabilized method Exponential scalar auxiliary variable |
Publisher: | Springer | Journal: | Journal of scientific computing | ISSN: | 0885-7474 | DOI: | 10.1007/s10915-022-01921-9 | Rights: | © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use (https://www.springernature.com/gp/open-research/policies/accepted-manuscript-terms), but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s10915-022-01921-9. |
Appears in Collections: | Journal/Magazine Article |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Ju_Stabilized_Exponential-Sav_Schemes.pdf | Pre-Published version | 3.26 MB | Adobe PDF | View/Open |
Page views
54
Last Week
0
0
Last month
Citations as of May 19, 2024
Downloads
33
Citations as of May 19, 2024
SCOPUSTM
Citations
23
Citations as of May 17, 2024
WEB OF SCIENCETM
Citations
17
Citations as of May 16, 2024
Google ScholarTM
Check
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.