Error estimates to smooth solutions of high order Runge-Kutta discontinuous Galerkin methods for scalar nonlinear conservation laws with and without sonic points

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:2021-12-06 09:00


时  间:126日上午09:00

地  点:海韵园数理大楼6楼686会议室


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.


张强博士, 南京大学教授。1993 年毕业于南开大学数学系。1996 年和1999 年在南开大学分别获取计算数学硕士和博士学位。2000 9 月至2002 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 3 2004 8 月在新加坡国立大学计算科学系从事研究工作。19997 月留校在南开大学数学科学学院工作,2007 12 月应聘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。