Academic Report of School of Mathematical Sciences [2026] No. 065

(Series Report for High-Level University Construction No. 1324)

Title：Fully discrete continuous data assimilation algorithms for reaction-diffusion equations: error estimates and parameter recovery

Speaker：Wansheng Wang, Professor (Shanghai Normal University)

Time：16:30-17:30, June 26, 2026

Location：Conference Room 308, Alumni Plaza, Yuehai Campus, Shenzhen University

Abstract: The purpose of this study is to provided error estimates for 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.

Speaker Profile：Professor at Shanghai Normal University; doctoral advisor; Director of the Office of Undergraduate Teaching Quality Management; Deputy Director of the Office of Academic Affairs; and Director of the Institute of Mathematical Sciences. He received his Ph.D. from Xiangtan University in June 2008 and completed postdoctoral fellowships at Huazhong University of Science and Technology and the University of Cambridge. His teaching and research focus primarily on numerical methods for differential equations and their applications. He has made significant contributions in the theoretical analysis and fast algorithms for financial option models, stability-preserving and adaptive algorithms for differential equations, data assimilation, and deep learning algorithms. As the first author, he has published over 120 academic papers in journals such as Numer. Math., SIAM J. Numer. Anal., Math. Comput., SIAM J. Sci. Comput., and Inver. Problem as first author. As the principal investigator, he has received one Second Prize in the Shanghai Natural Science Award and one Second Prize in the Hunan Natural Science Award, as well as the Fok Ying Tung Young Teacher Award. He has led four projects funded by the National Natural Science Foundation of China, as well as research projects such as the Hunan Provincial High-Level Talent Program. He has visited prestigious universities both domestically and internationally, including Peking University, the University of California, Irvine, and the University of Cambridge. He has been selected for talent programs such as Hunan Province’s New Century “121 Talent Project.” He serves on the editorial board of AAMM, chairs the Simulation Algorithms Specialized Committee of the China Society for Simulation, serves as a council member of the China Society for Simulation, is a standing committee member of the FinTech and Algorithms Specialized Committee of the Chinese Society for Industrial and Applied Mathematics, and is a council member of the Computational Mathematics Branch of the Chinese Mathematical Society.

Faculty and students are welcome to attend!

Invited by: Jian Lu

School of Mathematical Sciences

June 25, 2026