带乘性噪声的随机Allen-Cahn方程有效完全离散化的强收敛性

IF 3.8 2区 数学 Q1 MATHEMATICS, APPLIED
Xiao Qi , Lihua Wang , Yubin Yan
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引用次数: 0

摘要

本文研究了由乘性噪声驱动的随机Allen-Cahn方程在时间上基于半隐式的收敛方法和空间上基于截断噪声的有限元方法的完全离散化的强收敛性。所提出的全离散格式具有较低的计算复杂度和均方无条件稳定性。由于无穷维乘性驱动噪声和三次非线性漂移项带来的非全局Lipschitz困难,使得全离散解的强收敛性分析相当复杂。通过构造适当的辅助程序,巧妙地分解了全离散化误差,并在一定的弱假设条件下成功地导出了时空强收敛阶数。最后通过数值实验对理论结果进行了验证。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Strong convergence for efficient full discretization of the stochastic Allen–Cahn equation with multiplicative noise
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 introduced 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.
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来源期刊
Communications in Nonlinear Science and Numerical Simulation
Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
CiteScore
6.80
自引率
7.70%
发文量
378
审稿时长
78 days
期刊介绍: The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.
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