报告人：张强教授（南京大学）

报告题目：Stability analysis of Runge-Kutta discontinuous Galerkin methods for two-dimensional hyperbolic equations

报告摘要：(1) In this talk, we shall present the L^2-norm stability analysis of the Runge-Kutta discontinuous Galerkin (RKDG) methods on rectangle meshes when solving a linear constant coefficient hyperbolic equation, where the matrix transferring process based on temporal differences of stage solutions still plays an important role to achieve a nice energy equation for carrying out the energy analysis.

(2) In addition, this extension looks easy for most cases; however, there are a few troubles to obtaining good stability results under a standard CFL condition, especially for those Q^k-elements with lower degree k as that stated in one-dimensional case. This difficulty can be addressed by making full use of the commutative property of the spatial DG derivative operators along two directions and set up a new proof line to accomplish the purpose. Numerical experiments illustrating the robustness of our method are also provided.

报告时间：2024年8月6日9:00-12:00

报告地点：理学楼501室

报告人简介：张强，1989年就读于南开大学数学系，直至1999年博士毕业留校；2000-2002年在中国科学技术大学数学系博士后；2008年至今，南京大学数学系教授。一直从事偏微分方程数值方法研究，特别是间断有限元全离散格式的理论分析和实际应⽤。主持和参与多项国家自然科学基金项目，发表学术论文50多篇。