报告题目：Weak convergence of a full-discretization to stochastic Allen–Cahn equation driven by multiplicative noise

报 告 人：张敏行 (PhD Student @ JLU – Jilin University)

报告时间：2026年3月12日（星期四）9:00—9:45

报告地点：数学科学学院114（小报告厅）      

校内联系人：廖娴 教授       联系方式：84708351-8510

Abstract: In this talk, I will present recent work on numerical approximations of the stochastic Allen–Cahn equation driven by multiplicative trace-class noise. We consider a fully discrete scheme combining a drift-implicit Euler method in time with a spectral Galerkin approximation in space.  The main focus is on weak convergence analysis. I will explain how the spatial weak convergence rate improves upon the corresponding strong rate—by nearly one order in dimensions d =1,2 and by nearly one-half order in dimension d=3. For the temporal discretization, we obtain weak convergence rates close to order one in d=1,2$and close to 3/4 in d=3. A key ingredient of the analysis is the derivation of suitable a priori estimates for the Kolmogorov equations associated with the spectral Galerkin semi-discretization. In addition, I will introduce techniques for handling operator traces involving stochastic integrals in the temporal weak error analysis.