Speaker：Qiang Zhang（Nanjing University）

Time：2021-05-21 10:30

Location：Conference Room 313 at Administration Building at Haiyun Campus

Abstract:

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.