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：邹永魁 教授（吉林大学）

报告时间：2025年6月2日（星期一）10：00

报告地点：数学科学学院114      

校内联系人： 李崇君 教授   联系方式：84708351-8310

报告摘要：In this talk, 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 full-discretized 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 semi-discretization. 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 some numerical experiments to illustrate the theoretical analysis.

报告人简介：邹永魁，吉林大学数学学院教授，博士生导师。主要从事动力系统分支理论数值方法的研究、偏微分方程数值算法的研究，随机偏微分方程的数值方法研究、非线性滤波问题数值方法的研究。曾获教育部科学进步奖三等奖、入选教育部新世纪优秀人次资助计划、第七届吉林省教学成果奖一等奖、吉林省优秀教师，主持和参与多项国家级科研项目，发表学术论文40余篇，出版国家级规划教材1部参编多部教材。