Speaker：Qiang Zhang（Nanjing University）

Time：2021-12-06 09:00

Location：Conference Room 686 at the 6th floor of Shuli Building at Haiyun Campus

Abstract:

In this talk we present an a priori L1(L2)-norm error estimates of the fourth order Runge{Kutta discontinuous Galerkin method, as an example, for solving sufficiently smooth solutions of one-dimensional scalar nonlinear conservation laws. The optimal order of accuracy in time is obtained under the standard Courant-Friedrichs-Lewy condition, and the quasi-optimal and/or the optimal order of accuracy in space are achieved for many widelyused numerical fluxes, no matter whether the sonic points emerges or not. To prove the above result, we adopt the matrix transferring process from the linear constant case to the nonlinear case, and propose the generalized Gauss-Radau projection of the reference functions. The projection strongly depends on the relative upwind effect and its sharp approximation property is hard to obtain, especially when the sonic point emerges. Finally, some numerical experiments are given to support our theoretical results.