报告题目1：A decoupled stabilized finite element method for the time dependent Navier-Stokes/Biot problem

报告人：郭利明 博士

报告时间：2024年4月2日14：30—16：30

报告地点：威廉希尔315报告厅

报告摘要：In this paper, we propose a decoupled stabilized finite element method for the time dependent Navier-Stokes/Biot problem by using  the lowest equal-order finite elements. The coupling problem is divided into two subproblems which can be solved in parallel: one is the Navier-Stokes model by treating the nonlinear term explicitly, and the other is the Biot model. In this numerical scheme, we use the  backward Euler formula to implicitly obtain the solutions in time, while treats the coupling terms explicitly. The stability analysis and  error estimates are established for the proposed fully-discrete scheme. Numerical results are provided to justify the theory.

郭利明，博士，2015年获得同济大学理学博士学位，主要从事偏微分方程数值解等方面的研究，主持在研国家自然科学基金青年项目一项。在学术期刊Computers & Mathematics with Applications， Numerical Methods for Partial Differential Equations，Journal of Computational and Applied Mathematics等发表SCI论文7篇。

报告题目2：Block implicit methods for parabolic equations

报告人：李世顺 英国威廉希尔公司特聘教授

报告时间：2024年4月2日14：30—16：30

报告地点：威廉希尔315报告厅

报告摘要：One step block implicit methods (BIM) have desirable stability properties and provide higher-order of accuracy. In this talk, we first introduce several traditional time-stepping algorithms. Then we present a family of BIM designed with a positive definite matrix and a positive diagonal matrix; both matrix properties are desirable but not available in Runge-Kutta methods. Further, we show that the traditional finite element theory for parabolic problems discretized by the backward Euler or Crank-Nicolson schemes can also be extended for BIM.. Finally, some numerical results are reported to demonstrate the effectiveness of BIM.

李世顺，英国威廉希尔公司特聘教授。2011年6月博士毕业于浙江大学数学系。2013年11月-2014年11月美国科罗拉多大学计算机系博士后，2018年1月-2018年12月中国科学院深圳先进技术研究院访问学者。2020年7月-2020年12月澳门大学访问学者。研究方向为区域分解方法和并行算法。目前主要研究时空并行区域分解算法的理论与应用。