报告题目: An oscillation-free discontinuous Galerkin method for hyperbolic conservation laws

报告人：卢键方（华南理工大学）

时间：1月23日上午10:30-11:30

地点：五教5305教室

摘要：

In this talk, we introduce an oscillation-free discontinuous Galerkin (OFDG) method for solving the hyperbolic conservation laws. Typically, the high order linear numerical schemes would generate spurious oscillations in the presence of discontinuous solutions. The spurious oscillations can be harmful to the numerical simulation, as they not only generate some non-physical structures but also cause many overshoots and undershoots that make the numerical scheme less robust. To overcome this difficulty, we incorporate a numerical damping term into the classic DG formulation to control spurious oscillations. With this modification, the proposed DG method still maintains many good properties, such as the extremely local data structure, conservation, $L^2$-boundedness, optimal error estimates, and superconvergence. A series of numerical examples are provided, which not only demonstrate the superior performance of the scheme but also confirm the derived theoretical results, thus validating the effectiveness of the proposed DG scheme.

报告人简介：

卢键方博士于2010年在中国科学技术大学获得理学学士学位，2016年博士毕业于中国科学技术大学，2016至2018年在北京计算科学研究中心做博士后，2018年至2021年在华南师范大学华南数学应用与交叉研究中心当讲师，2021年8月至今在华南理工大学数学学院任副教授。研究兴趣包括流体力学的高精度数值算法和非局部扩散方程的间断有限元方法。