报告人：张强教授

报告题目：Error estimate to smooth solutions of high order Runge-Kutta discontinuous Galerkin method for scalar nonlinear conservation laws with and without sonic points

报告摘要：

(1) In this talk, we shall take the fourth order in time Runge-Kutta discontinuous Galerkin method, as an example, to establish a sharp 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 widely-used numerical fluxes, no matter whether the solution contains sonic points or not.

(2) The main tools include the matrix transferring process based on temporal differences of stage solutions, as well as the generalized Gauss-Radau projection of the reference functions that strongly depends on the relative upwind effect of the used numerical flux. Finally, we show some numerical examples to support theoretical results.

报告时间：2022年10月29日上午10:00-13:00

报告形式：腾讯会议；会议号：220-489-709

获取会议密码请发邮件至：liuwenjie@hit.edu.cn

报告人简介：张强，1989-1999年于南开大学数学系本硕博，1999年留校任教；2000-2002年在中国科学技术大学博士后；2008年至今，任职南京大学数学系教授。从事偏微分方程的数值解法研究，特别是间断有限元全离散格式的理论分析和实际应用。主持参与多项国家自然科学基金项目，共发表学术论文40多篇。