Superconvergence analysis on the Runge-Kutta discontinuous Galerkin method for two-dimensional linear hyperbolic equation

：张强
：2021-05-21 10:30
：厦大海韵园行政楼B313

报告人：张强（南京大学）

时  间：5月21日上午10:30

地  点：厦大海韵园行政楼B313

内容摘要:

In this talk we shall report some convergence results on the Runge-  Kutta discontinuous Galerkin (RKDG) method to solve two-dimensional lin- ear constant-coefficient hyperbolic equation, in which the upwind-biased nu- merical flux and the explicit Runge-Kutta time-marching are used. Firstly, we set up a unified framework to investigate the L2-norm stability of the RKDG method with arbitrary stage and arbitrary order in time as well as the arbitrary degree of piecewise polynomials, where the main development is the matrix transferring process based on the temporal differences of stage solutions. By virtue of the incomplete correction technique to the reference functions at every time stage, as well as the generalized Gauss-Radau pro- jection, we are able to establish the superconvergence results for the RKDG method in a mild regularity assumption on the exact solution that is indepen- dent of the stage number. Namely, the RKDG method perfectly preserves the superconvergence performance of the semi-discrete method, and the time discretization solely produces an optimal error order in time. Finally, some numerical experiments are given.

个人简介：

张强，南京大学教授，1993年、1996 年和1999 年在南开大学数学系分别获取计算数学学士、硕士和博士学位。2000 年9 月至2002 年7 月在中国科学技术大学数学系长江学者舒其望教授的指导下从事博士后研究工作。2004 年3 至2004 年8 月在新加坡国立大学计算科学系从事研究工作。1999年7 月留校在南开大学数学科学学院工作，2008 年03 月到南京大学数学系工作，任职教授。长期从事发展型方程有限元方法的理论分析工作, 特别是在间断Galerkin有限元的理论分析工作取得了一些突破性进展。

 

联系人：邱建贤