应哈尔滨工业大学数学学院吴勃英、张达治老师邀请，南京大学数学系张强教授作学术报告，欢迎感兴趣的师生参加！

【报告题目】：

1、Stability analysis of Runge-Kutta discontinuous Galerkin method for linear hyperbolic equation

2、Error estimates of Runge-Kutta discontinuous Galerkin method for linear hyperbolic equation

【报告时间】：2020年5月15日下午14：00

【报告平台】：腾讯会议

点击链接直接加入会议：https://meeting.tencent.com/s/51aS6oVfa28f

【会议】：381 708 225

【报告摘要】：In this talk we present some analysis techniques and theory results on the Runge-Kutta discontinuous Galerkin (RKDG) method with the upwind-biased numerical flux and the explicit Runge-Kutta algorithm, when solving the linear constant-coefficient hyperbolic equation. Firstly we set up a unified framework to investigate the L2-norm stability, by the help of an matrix transferring process based on the temporal differences of stage solutions. Different types of stability performance are shown for many popular schemes. Then we establish the optimal L2-norm error estimate in both time and space under a mild smoothness assumption of exact solution, which is independent of the stages number of RKDG methods. The main tools are the above stability analysis and the generalized Gauss-Radau projection to the reference functions at stage time. Finally we give some superconvergence results of RKDG methods by using the incomplete correction function technique.

【报告人简介】：张强，南京大学教授，博士生导师。于1989年就读南开大学数学系，直到1999年博士毕业留校任教，2008年到南京大学任教授至今。长期关注发展偏微分方程的数值方法，特别是对流占优扩散方程以及双曲守恒律方程的稳定化有限元方法。近期的工作集中于间断有限元方法，在SIAM Journal on Numerical Analysis，Numerische Mathematik，和Journal of Scientific Computing等国际著名期刊上发表论文50余篇。主持4项国家自然科学基金项目，参与1项国家自然科学基金重点项目。