Speaker: Professor Weizhu Bao，National University of Singapore

Title: Structure-preserving parametric finite element methods for geometric PDEs and applications

Language: Chinese

Time & Venue: 2026.03.24 16:00 数学院南楼N219

Abstract: In this talk, I begin with a review of different geometric flows (PDEs) including mean curvature (curve shortening) flow, surface diffusion flow, Willmore flow, Gauss curvature flow, etc., which arise from materials science, interface dynamics in multi-phase flows, biology membrane, computer graphics, geometry,etc. Different mathematical formulations and numerical methods for mean curvature flow are then discussed. In particular, an energy-stable linearly implicit parametric finite element method (PFEM) is presented in details. Then the PFEM is extended to surface diffusion flow and anisotropic surface diffusion flow, and a structure-preserving implicit PFEM is proposed. Finally, sharp interface models and their PFEM approximations are presented for solid-state dewetting. This talk is based on joint works with Harald Garcke, Wei Jiang, Yifei Li, Robert Nuernberg, Tiezheng Qian, David Srolovitz, Dongmin Wang, Yan Wang and Quan Zhao.