應(yīng)yl7703永利官網(wǎng)邀請，寧波東方理工大學沈捷教授將于2024年7月16日舉辦線上學術(shù)報告。歡迎廣大師生參加。

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

時間：2024年7月16日10:05

騰訊會議ID：623727979 密碼：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.

報告人簡介

沈捷教授現(xiàn)為寧波東方理工大學講席教授和數(shù)學科學學院院長。他于1982年畢業(yè)于北京大學計算數(shù)學專業(yè), 1987年獲法國巴黎十一大學博士學位，于1987年獲得博士學位后赴美國Indiana University從事博士后研究。2009年入選國家級海外高層次人才項目，2017年當選美國數(shù)學會AMS fellow，2020當選國際工業(yè)與應(yīng)用數(shù)學協(xié)會SIAM fellow，2023年全職回國前為普渡大學杰出教授。沈捷教授主要從事偏微分方程數(shù)值解研究工作，具體研究方向包括譜方法數(shù)值分析理論,計算流體,以及計算材料科學。在國際雜志上發(fā)表了兩百多篇論文，兩本專著，在谷歌學術(shù)的引用逾2萬七千余次。

甘肅省高校應(yīng)用數(shù)學與復雜系統(tǒng)省級重點實驗室

甘肅應(yīng)用數(shù)學中心

yl7703永利官網(wǎng)

萃英學院

2024年7月15日