报告题目： Weak Convergence of Drift-Implicit Euler and Spectral Galerkin Approximation to Stochastic Allen-Cahn Equation Driven by Multiplicative Trace-Class Noise

报 告 人：Cao Yanzhao 教授 奥本大学

讲授时间：2025年6月30日，14:00--15:00

授课地点：数学楼3楼研讨室4

校内联系人：邹永魁 [email protected]

Abstract： In this paper, we are concerned with a stochastic Allen-Cahn equation driven by a multiplicative trace-class noise in a multi-dimensional setting. We apply a drift-implicit Euler scheme and a spectral Galerkin method to construct a fulldiscretized scheme. Our main purpose is to investigate the weak convergence order by means of the theory of Kolmogorov equation and Malliavin calculus. We overcome the challenge of spatial weak error analysis by deriving estimates for solutions to the Kolmogorov equations related to spectral Galerkin semidiscretization. We also manage to address the challenge of temporal weak error estimate by dealing with the trace of an operator which is the product of three operators and one of them includes an item of stochastic integral. We prove that the spatial weak convergence rate is almost one order higher than exact solution’s regularity and the temporal weak convergence rate is of almost 1. Finally, we present a numerical experiment to illustrate the theoretical analysis.

报告人简介：曹延昭教授，1983年毕业于成人直播平台 数学系，1996年获弗吉尼亚理工学院数学博士学位，现任美国奥本大学数学与统计学系 Don Logan endowed chair professor.应用与工业数学学会（SIAM）美国东南地区分会主席。主要从事偏微分方程和积分方程数值解法、随机偏微分方程数值解、非线性滤波、不确定性量化等领域的研究，部分研究成果发表在《SIAM J. Numer. Anal.》、《Numer. Math.》、《Math. Comp.》、《IMA J. Numer. Anal.》等计算数学顶级期刊上。