张强: Optimal error estimate of the explicit DG method

报告时间：2024年11月29日（星期五）15:00 报告地点：科教楼B1710室 报 告 人：张强 教授 工作单位：南京⼤学 举办单位：数学学院 报告简介： In this talk, we consider the explicit single-step discontinuous Galerkin (DG) method with stage- dependent flux parameters, when solving a linear constant-coefficient hyperbolic equation in one dimension. Two well-known examples of this method include the Runge-Kutta DG method with the downwind treatment for the negative time marching coefficients, as well as the Lax-Wendroff DG method with arbitrary numerical flux parameters for auxiliary variables. By the matrix transferring process based on the temporal differences of stage solutions, we find that the stability performance of this method depends on the averaged numerical flux parameter. To obtain the optimal error estimate, we have to present a novel way to obtain the optimal error estimate in both space and time. The main tool is a series of space-time approximation functions for a given spatial function. Finally, some numerical experiments are given to validate the theoretical results. 报告人简介： 张强，1989-1999年南开⼤学数学系本硕博，1999年南京大学任教；2000-2002年中国科学技术⼤学博⼠后； 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，特别关注间断有限元方法的分析和应⽤。主持参与多项国家⾃然科学基⾦项⽬，发表学术论⽂50多篇。