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Strong convergence for efficient full discretization of the stochastic Allen-Cahn equation with multiplicative noise

Qi, Xiao
; 
Wang, Lihua
; 
Yan, Yubin
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Affiliation
Jianghan University; University of Chester
EPub Date
Publication Date
2025-04-25
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Computer Science
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Abstract
In this paper, we study the strong convergence of the full discretization based on a semi-implicit tamed approach in time and the finite element method with truncated noise in space for the stochastic Allen-Cahn equation driven by multiplicative noise. The proposed fully discrete scheme is efficient thanks to its low computational complexity and mean-square unconditional stability. The low regularity of the solution due to the multiplicative infinite-dimensional driving noise and the non-global Lipschitz difficulty intruduced by the cubic nonlinear drift term make the strong convergence analysis of the fully discrete solution considerably complicated. By constructing an appropriate auxiliary procedure, the full discretization error can be cleverly decomposed, and the spatio-temporal strong convergence order is successfully derived under certain weak assumptions. Numerical experiments are finally reported to validate the theoretical result.
Citation
Qi, X., Wang, L., & Yan, Y. (2025). Strong convergence for efficient full discretization of the stochastic Allen-Cahn equation with multiplicative noise. Communications in Nonlinear Science and Numerical Simulation, 148, article-number 108860. https://doi.org/10.1016/j.cnsns.2025.108860
Publisher
Elsevier
Journal
Communications in Nonlinear Science and Numerical Simulation
Research Unit
URI
http://hdl.handle.net/10034/629395
DOI
10.1016/j.cnsns.2025.108860
PubMed ID
PubMed Central ID
Type
Article
Language
en
Description
© 2025 The Authors. Published by Elsevier B.V.
Series/Report no.
ISSN
1007-5704
EISSN
1878-7274
ISBN
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Sponsors
Financial support was provided by the Research Fund of Jianghan University under Grant No. 2024JCYJ04
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https://www.sciencedirect.com/science/article/pii/S1007570425002710?via%3Dihub