Buyang Li, Associate Professor, Hong Kong Polytechnic University

Haijun Yu, Professor

Evolving finite element methods with an artificial tangential velocity for mean curvature flow and Willmore flow

10:00-11:00 May 17 (Wednesday), Z311

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.

Bio: Dr. Buyang Li received his Ph.D. degree from the City University of Hong Kong in 2012. After obtaining his PhD, he has been  engaged in scientific research and teaching at Nanjing University, University of Tubingen (Germany), and Hong Kong Polytechnic University. Currently, he is an associate professor in the Department of Applied Mathematics at the Hong Kong Polytechnic University. His research areas are scientific computing and numerical analysis for partial differential equations from geometry, physics, and industrial applications, including finite element approximation of surface evolution under geometric flow, numerical approximation of rough solutions of nonlinear dispersion and wave equations, numerical methods and analysis for incompressible Navier-Stokes equations, perfectly matched layer methods for high frequency Helmholtz equations, and numerical solutions of nonlinear parabolic and fractional partial differential equations, Ginzburg-Landau superconductivity equations, thermistor equations, etc.