Speaker：Dr. Buyang Li (李步阳博士)
Time：15:00-15:40, 18 November 2019 (Monday) (Beijing time)
Venue：T2-202
We propose a new method to approximate the mean curvature flow of closed two-dimensional surfaces. The numerical method proposed and studied here combines evolving finite elements, whose nodes determine the discrete surface like in Dziuk’s method, and linearly implicit backward difference formulae for time integration. The proposed method differs from Dziuk’s approach in that it discretizes Huisken’s evolution equations for the normal vector and mean curvature and uses these evolving geometric quantities in the velocity law projected to the finite element space. This numerical method admits a convergence analysis in the case of finite elements of polynomial degree at least two and backward difference formulae of orders two to five. The error analysis combines stability estimates and consistency estimates to yield optimal-order H1-norm error bounds for the computed surface position, velocity, normal vector and mean curvature. The stability analysis is based on the matrix–vector formulation of the finite element method and does not use geometric arguments. The geometry enters only into the consistency estimates. Numerical experiments illustrate and complement the theoretical results.
About Dr. Li
Dr. Buyang Li got his PhD in City University of Hong Kong in 2012. From 2012 to 2015 he worked in Nanjing University as Assistant Professor, and in 2015-2016 he was Humboldt Research Fellow at University of Tuebingen. From 2016 to present, he worked in The Hong Kong Polytechnic University as Assistant Professor. Buyang Li’s research interest is developing novel numerical methods for solving nonlinear partial differential equations in physics and geometry.
