报告问题 (Title)：Analysis of fully discrete finite element methods for 2D Navier--Stokes equations with critical initial data(具有临界初始值的二维Navier-Stokes方程的全离散有限元法的剖析)

报告人 (Speaker)： 李步扬 副教授（香港理工大学）

报告时间 (Time)：2022年9月9日(周五) 14:00-16:00

报告所在 (Place)：线上腾讯聚会 （聚会 ID：963 935 431）

约请人(Inviter)：李常品、蔡敏

主理部分：理学院数学系

报告摘要：First-order convergence in time and space is proved for a fully discrete semi-implicit 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 $t_m$ is smaller than some constant. Numerical examples are provided to support the theoretical analysis.