Seminars on Numerical Algorithms, Analyses, and Applications:An oscillation-free discontinuous Galerkin method for hyperbolic conservation laws

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:卢键方(华南理工大学)
:2022-12-02 15:00
:腾讯会议ID:800-110-721(无密码)

报告人:卢键方(华南理工大学)

时  间:122日下午15:00-16:30

地  点:腾讯会议ID800-110-721(无密码)

内容摘要:

In this talk, we propose an oscillation-free discontinuous Galerkin (OFDG) 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 contains discontinuities. The spurious oscillations maybe harmful to the numerical simulation, as it not only generates some artificial structures not belonging to the problems, but also causes many overshoots and undershoots that make the numerical scheme less robust. 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, $L^2$-boundedness, optimal error estimates and superconvergence. We also provide some numerical examples to show the good performance of the proposed DG scheme and verify our theoretical results.

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,20162018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,20218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。已在SIAM Journal of Scientific Computing, SIAM Journal of Numerical Analysis, Mathematics of Computation等期刊发表多篇文章。

 

联系人:熊涛