报告时间：2022年06月21日（星期二）15:00-16:00

报告地点：腾讯会议 819185610

报 告 人：张强 教授

工作单位：南京大学

举办单位：数学与统计学院

报告简介：

In this talk, we shall take the fourth order in time Runge-Kutta discontinuous Galerkin method, as an example of high order schemes, to establish an a priori L2-norm error estimate for sufficiently smooth solutions of one-dimensional scalar nonlinear conservation laws. The optimal order of accuracy in time is obtained under the standard CFL condition, and the quasi-optimal and/or optimal order of accuracy in space is achieved for many widely-used numerical fluxes, no matter whether the exact solution contains sonic points or not. The main tools are the matrix transferring process based on the temporal differences of stage solutions, and the generalized Gauss-Radau projection of the reference functions, strongly depending on the relative upwind effect of the numerical fluxes. Finally, we show some numerical examples to support the theoretical results.

报告人简介：

张强，1989-1999年在南开⼤学数学系本硕博，于1999年获博⼠学位并留校任教。2000-2002年在中国科学技术⼤学博⼠后。2008年至今在南京⼤学数学系任职教授。一直从事偏微分⽅程数值⽅法研究，⽬前重点关注间断有限元⽅法全离散格式的理论分析和实际应⽤。主持和参与多项国家⾃然科学基⾦项⽬，已发表学术论⽂40多篇。