Speaker: Zhang Qiang, professor and doctoral supervisor, Nanjing University

Date: November 24, 2024

Time: 9:00-10:00 am

Location: B919, Zhixin Building, Shandong University

Sponsor: School of Mathematics, Shandong University

Abstract:

In this talk, we consider the explicit single-step discontinuous Galerkin (DG) method with stage-dependent flux parameters, when solving a linear constant-coefficient hyperbolic equation in one dimension. Two well-known examples of this method include the Runge-Kutta DG method with the downwind treatment for the negative time marching coefficients, as well as the Lax-Wendroff DG method with arbitrary numerical flux parameters for auxiliary variables. By the matrix transferring process based on the temporal differences of stage solutions, we find that the stability performance of this method depends on the averaged numerical flux parameter. To obtain the optimal error estimate, we have to present a novel way to obtain the optimal error estimate in both space and time. The main tool is a series of space-time approximation functions for a given spatial function, which preserve the local structure of the numerical scheme and the balance of exact evolution under the control of the partial differential equation. Finally, some numerical experiments are given to validate the theoretical results.

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https://www.view.sdu.edu.cn/info/1020/197064.htm