Speaker：Prof. Zhang Qiang

          Nanjing University

Title: Theoretical analysis on the Runge{Kutta discontinuous Galerkin method for linear hyperbolic equation

Time：27^th, Nov., 2020, 16:00

Location：数理大楼天元会议室 (线下) 

Abstract:

In this talk we present some results on the Runge{Kutta discontinuous Galerkin (RKDG) method to solve the linear constant hyperbolic equation, where the time is advanced by the explicit Runge{Kutta algorithm with arbitrary stage number and time order. First we propose a unified framework to investigate the L2-norm stability performance of the RKDG methods, by using the matrix transferring process based on the temporal differences of stage solutions. By using the generalized Gauss-Radau projection to the reference functions at every time stage, we are able to set up the optimal L2-norm error estimate under the regularity assumption that is independent of the stage number. By virtue of the incomplete correction technique, we can theoretically show that the superconvergence performance of the semidiscrete DG method is perfectly preserved by the RKDG method and the time discretization solely produces an optimal error order in time.

Speaker Introduction：

张强，博士，南京大学教授，博士生导师，长期从事发展型偏微分方程的数值方法研究，特别是对流占优的扩散方程以及双曲守恒律方程的非标准有限元方法。文章多发表在SIAM J. Numer Anal., Numer. Math.,和J. Sci. Comp.等国际著名期刊上。

联系人：邱建贤