Keynote Speaker:Wang Jilu

Abstract:

An implicit energy-decaying modified Crank-Nicolson time-stepping method is constructed for the viscous rotating shallow water equation on the plane. Existence, uniqueness and convergence of semidiscrete solutions are proved by using Schaefer's fixed point theorem and $H^2$ estimates of the discretized hyperbolic-parabolic system. For practical computation, the semidiscrete method is further discretized in space, resulting in a fully discrete energy-decaying finite element scheme. A fixed-point iterative method is proposed for solving the nonlinear algebraic system. The numerical results show that the proposed method requires only a few iterations to achieve the desired accuracy, with second-order convergence in time, and preserves energy decay well.

Speaker Introduction:

Wang Jilu, a distinguished researcher of Beijing Computational Science Research Center, received a bachelor's degree from Shandong University in 2011 and a doctor's degree from City University of Hong Kong in 2015. He worked as a post-doctoral researcher at Florida State University from 2016 to 2018 and a visiting assistant professor at Mississippi State University from 2018 to 2019. His research projects mainly focus on the numerical solution of partial differential equation, specifically including the error estimation of finite element methods for incompressible miscible driving models, shallow water waves, Schrodinger's equation and fractional order equations in porous media, which have been published in international famous journals such asSIAM J. Numer. Anal.,Numer. Math.,Math. Comput.

Inviter:

Jiang Xiaoyun ProfessorofSchool of Mathematics

Time:

9:00-9:50on November 28 (Saturday)

Location:

Tencent Meeting, Meeting ID:782 591 290

Click the link to attend the meeting, or add to the meeting list:

https://meeting.tencent.com/s/kXABuXE4hbgt

Hosted by: School of Mathematics, Shandong University