报告题目 (Title)：Model and data-driven fully discrete continuous data assimilation algorithms: error estimates and parameter recovery (模型和数据驱动的完全离散连续数据同化算法：误差估计和参数恢复)

报告人 (Speaker)：王晚生教授 (上海师范大学)

报告时间 (Time)：2025年11月13日（周四）10:00

报告地点 (Place)：腾讯会议 985 273 770

邀请人(Inviter)：朱佩成

主办部门：理学院数学系

报告摘要：

The purpose of this study is to provided error estimates for model and data-driven fully discrete continuous data assimilation algorithms for reaction-diffusion equations and recover the diffuse interface width parameter for nonlinear Allen-Cahn equation by a continuous data assimilation algorithm proposed recently. We obtain the large-time error between the true solution of the Allen-Cahn equation and the data assimilated solution produced by implicit-explicit (IMEX) one-leg fully discrete finite element methods due to discrepancy between an approximate diffuse interface width and the physical interface width. The strongly $A$-stability of the one-leg methods plays key roles in proving the exponential decay of initial error. Based on the long-time error estimates, we develop several algorithms to recover both the true solution and the true diffuse interface width using only spatially discrete phase field function measurements. Numerical experiments confirm our theoretical results and verify the effectiveness of the proposed methods.