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

报告人：刘勇 （中科院数学与系统科学研究院）

报告时间：4月6日 16:00

报告地点：管理楼1418 

摘要：

In this talk, we propose a novel discontinuous Galerkin (DG) method to control the spurious oscillations when solving the hyperbolic conservation laws. The spurious oscillations may be 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. Compared 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 also extend our methods to systems of hyperbolic conservation laws.

Entropy inequalities are crucial to the well-posedness of hyperbolic conservation laws, which help to select the physically meaningful one among the infinite many weak solutions. By combining with quadrature-based entropy-stable DG methods, we also developed the entropy-stable OFDG method. For time discretizations, the modified exponential Runge--Kutta method can 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. This is a joint work with Jianfang Lu (SCUT) and Chi-Wang Shu (Brown Univ.).

报告人简介：刘勇，中科院数学与系统科学研究院，计算数学所，副研究员。分别于2015年，2020年获中国科学技术大学学士和博士学位。2018年至2020年在美国布朗大学应用数学系联合培养。2020年至2022年在中科院数学与系统科学研究院，华罗庚数学科学中心做博士后。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、非拟合网格有限元方法等。曾获2020年中科院院长奖特别奖，2021年中科院优博。主持国家自然科学基金青年项目，入选中科院青年创新促进会，入选中科院数学与系统科学研究院“陈景润未来之星”人才计划。在SINUM, SISC, JCP等SCI期刊发表论文10余篇。