Abstract

In this talk, I will introduce a novel discontinuous Galerkin (DG) method to control the spurious oscillations when solving the hyperbolic conservation laws. Usually, the high order linear numerical schemes would generate spurious oscillations when the solution of the hyperbolic conservation laws contains discontinuities. To overcome this difficulty, we introduce a numerical damping term to control spurious oscillations based on the classic DG formulation. Comparing to the classic DG method, the proposed DG method still maintains many good properties, such as the extremely local data structure, conservation, L2-boundedness, optimal error estimates and superconvergence. We use both the classical Runge-Kutta method and the modified exponential Runge-Kutta method in time discretization. Particularly, the latter one could avoid additional restrictions of time step size due to the numerical damping. Extensive numerical experiments are shown to demonstrate our algorithm is robust and effective.

个人简介：刘勇，中国科学院数学与系统科学研究院，华罗庚数学中心博士后。分别于2015年，2020年获中国科学技术大学学士和博士学位。2018年--2020年在美国布朗大学应用数学系联合培养。主要研究领域为高精度数值计算方法，包括间断有限元方法的算法设计及其数值分析、磁流体力学方程的数值模拟及应用等方面。在SIAM Journal on Numerical Analysis, SIAM Journal on Scientific Computing, Journal of Computational Physics等杂志发表论文10余篇。