Keynote Speaker:Zhang Qiang

Abstract:

In this talk we shall report some convergence results on the Runge-Kutta discontinuous Galerkin (RKDG) method to solve linear constant-coefficient hyperbolic equation. The numerical flux is upwind-biased and the time is advanced by the explicit Runge-Kutta algorithm. First we present a unified framework to investigate the L2 -norm stability performance. The main development is the matrix transferring process based on the temporal differences of stage solutions, which can be employed for any RKDG method with arbitrary stage and order. By the generalized Gauss-Radau projection to the reference functions at time stage, we are able to set up the L2 -norm error estimate. This conclusion is optimal in time and space, and is independent of the stage number. Based on the above studies, we can establish the superconvergence results by virtue of the incomplete correction technique to the above reference functions. The conclusion shows that the superconvergence performance of the semi-discrete DG method is perfectly preserved and the time discretization solely produces an optimal error order in time. Finally, some numerical experiments are given.

Introduction to the Speaker:

Zhang Qiang, Professor and Doctoral Supervisor of Nanjing University. He studied in the Department of mathematics of Nankai University in 1989. He got his doctor's degree in Computational Mathematics in 1999 and stayed in the university to teach. From 2000 to 2002, he carried out postdoctoral research in the University of Science and Technology of China. He has been a professor in Nanjing University since February 2008 and employed as a doctoral supervisor in 2009. For a long time, attention has been paid to the numerical methods of the evolutionary partial differential equations, especially the convection-dominated diffusion equations and the stabilized finite element methods for hyperbolic system of conservation laws. At present, his attention has been paid to the theoretical analysis and specific application of the full discretization of discontinuous FEM. He has presided over and participated in a number of general projects of National Natural Science Foundation of China (NSFC), and published more than 40 high-quality papers.

Inviter:

Gao Fuzheng, Professor of School of Mathematics

Time:

15:30-16:30 on October 7 (Wednesday)

Location:

Tencent Meeting, ID: 552 249 727

Sponsored by: School of Mathematics, Shandong University