应兰州大学数学与统计学院邀请，宁波东方理工大学沈捷教授将于2024年7月16日举办线上学术报告。欢迎广大师生参加。

题目：A new class of higher-order stiffly stable schemes with application to the Navier-Stokes equations

时间：2024年7月16日10:05

腾讯会议ID：623727979 密码：2407

摘要：How to construct stable second- and higher-order fully decoupled schemes for the incompressible Navier-Stokes equations has been a long standing open problem. A main issue is that stability regions of usual multistep time discretization decrease as their order of accuracy increase, so they do not possess enough stability to control the higher-order explicit treatment of the pressure in a fully decoupled scheme.

We shall construct a new class of IMEX schemes, by using Taylor expansion at $t_{n+\beta}$ (with $\beta\ge 1$ as a parameter) for updating the solution at $t_{n+1}$, whose stability region increases with $\beta$, thus allowing us to choose $\beta$ according to the stability and accuracy requirement. In particular, by choosing suitable $\beta$, we are able to construct higher-order unconditionally stable (in $H^1$ norm), fully decoupled consistent splitting schemes for the Navier-Stokes equations, and derive uniform optimal error estimates. We shall also present ample numerical results to show the computational advantages of these schemes for some nonlinear parabolic systems, including in particular Navier-Stokes equations.

报告人简介

沈捷教授现为宁波东方理工大学讲席教授和数学科学学院院长。他于1982年毕业于北京大学计算数学专业, 1987年获法国巴黎十一大学博士学位，于1987年获得博士学位后赴美国Indiana University从事博士后研究。2009年入选国家级海外高层次人才项目，2017年当选美国数学会AMS fellow，2020当选国际工业与应用数学协会SIAM fellow，2023年全职回国前为普渡大学杰出教授。沈捷教授主要从事偏微分方程数值解研究工作，具体研究方向包括谱方法数值分析理论,计算流体,以及计算材料科学。在国际杂志上发表了两百多篇论文，两本专著，在谷歌学术的引用逾2万七千余次。

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2024年7月15日