报告题目：Analysis of fully discrete finite element methods for 2D Navier-Stokes equations with critical initial data

报告人：李步扬

单位：香港理工大学

时间：2022年12月19日10:00

腾讯ID：926-153-668

摘要：First-order convergence in time and space is proved for a fully discrete semiimplicit finite element method for the two-dimensional Navier–Stokes equations with L^2 initial data in convex polygonal domains, without extra regularity assumptions or grid-ratio conditions. The proof utilises the smoothing properties of the Navier–Stokes equations in the analysis of the consistency errors, an appropriate duality argument, and the smallness of the numerical solution in the discrete L^2(0,t_m;H^1) norm when tm is smaller than some constant. Numerical examples are provided to support the theoretical analysis.

简介：Dr. Buyang Li received his Ph.D. degree from City University of Hong Kong in 2012. He 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.