讲座题目：Evolving finite element methods with an artificial tangential velocity for mean curvature flow and Willmore flow 主讲人：李步扬 副教授 主持人：朱升峰 教授 开始时间：2023-05-30 13:30:00 讲座地址：腾讯会议 529-614-510 主办单位：数学科学学院
报告人简介： Dr. Buyang Li received his Ph.D. degree from City University of Hong Kong in 2012. After obtaining his PhD degree, Dr. Li was engaged in scientific research and teaching at Nanjing University, University of Tübingen (Germany), and The Hong Kong Polytechnic University. He is currently an Associate Professor in the Department of Applied Mathematics, The Hong Kong Polytechnic University. His main research areas are scientific computing and numerical analysis for partial differential equations from geometry, physics and engineering applications, including finite element approximation of geometric curvature flow, numerical approximation of rough solutions of nonlinear dispersion and wave equations, numerical methods and analysis for incompressible Navier–Stokes equations, finite element and perfectly matched layer methods for high frequency Helmholtz equations, and numerical solution of nonlinear parabolic equations, phase field equations, fractional partial differential equations, Ginzburg-Landau superconductivity equations, thermistor equations, etc.
报告内容： An artificial tangential velocity is introduced into the evolving finite element methods for mean curvature flow and Willmore flow proposed by Kovács et al. (Numer Math 143(4), 797-853, 2019, Numer Math 149, 595-643, 2021) in order to improve the mesh quality in the computation. The artificial tangential velocity is constructed by considering a limiting situation in the method proposed by Barrett et al. (J Comput Phys 222(1), 441-467, 2007, J Comput Phys 227(9), 4281-4307, 2008, SIAM J Sci Comput 31(1), 225-253, 2008) . The stability of the artificial tangential velocity is proved. The optimal-order convergence of the evolving finite element methods with artificial tangential velocity are proved for both mean curvature flow and Willmore flow. Extensive numerical experiments are presented to illustrate the convergence of the method and the performance of the artificial tangential velocity in improving the mesh quality. |
