报告题目： Mesh-robust stability and convergence of variable-step BDF3 method

报告人：廖洪林 教授

时间：2023年9月22日下午：3:00-4:30

地点：本部维格堂319

摘要：

The third-order BDF (BDF3) scheme with variable steps are practically useful in time adaptive simulations for nonlinear gradient flows, hyperbolic systems with multiscale relaxation and stiff kinetic equations. We prove that the BDF3 scheme is stable for non-stiff problems if the adjacent step ratios are less than 2.553, and is stable for linear diffusion equations if the adjacent step ratios are less than 1.4877. Numerical tests show that the variable-step BDF3 method is mesh-robust with a desired convergence rate, even if many of step-ratios are much greater than our theoretical limits. Up to now, the  theoretical analysis remains incomplete so far, and mysterious to us.

This work is joint with undergradte student Li Zhaoyi, Prof. Tang Tao, and Prof. Zhou Tao.

个人简介：廖洪林，应用数学博士，2018年至今任教于南京航空航天大学数学学院。2001年在原解放军理工大学获理学硕士学位，2010年在东南大学获理学博士学位，2001-2017年任教于原解放军理工大学、解放军陆军工程大学。学术研究方向为微分方程数值解，目前主要关注相场以及多相流模型的时间变步长离散与自适应算法, 在Math Comp，SIAM J Numer Anal, SIAM J Sci Comput，J Comput Phys, IMA J Numer Anal，Sci China Math等国内外专业期刊上发表学术研究论文四十余篇。

邀请人：张亚楠