题目：Superconvergence analysis on the Runge-Kutta discontinuous Galerkin method for linear hyperbolic equation
报告人：张强（南京大学数学系）
时间：2021/01/18（周一）15:00-16:00（北京时间）
地点：腾讯会议
会议号：663 580 147
摘要：In this talk we shall report some convergence results on the Runge-Kutta discontinuous Galerkin (RKDG) method to solve linear constant-coefficient hyperbolic equation. The numerical flux is upwind-biased and the time is advanced by the explicit Runge-Kutta algorithm. First we present a unified framework to investigate the L^2-norm stability performance. The main development is the matrix transferring process based on the temporal differences of stage solutions, which can be employed for any RKDG method with arbitrary stage and order. By the generalized Gauss-Radau projection to the reference functions at time stage, we are able to set up the L^2-norm error estimate. This conclusion is optimal in time and space, and is independent of the stage number. Based on the above studies, we can establish the superconvergence results by virtue of the incomplete correction technique to the above reference functions. The conclusion shows that the superconvergence performance of the semi-discrete DG method is perfectly preserved and the time discretization solely produces an optimal error order in time. Finally, some numerical experiments are given.
报告人简介：张强，南京大学教授。主要研究方向是针对退化抛物方程、Sobolev类型的方程、流体动力学等相关方程的DG方法、Time-marching 方法、WENO 方法、Streamline 扩散有限元方法等，已在SIAM J.Numerical Analysis、JSC等杂志发表论文四十余篇。承担多项国家自然科学基金项目，目前为Communications on Applied Mathematices and Computation 的编委。
