针对双曲守恒律方程，系统探讨了间断有限元方法中的数值振荡问题。通过向格式中引入阻尼项，有效抑制了高阶多项式系数引起的非物理振荡，从而提出了一种本质无振荡的间断有限元方法。理论分析证明了该格式具有守恒性、熵稳定性，并获得了最优收敛阶及超收敛性质。该方法已成功应用于多种双曲守恒律系统，包括可压缩欧拉方程、浅水波方程、理想磁流体方程及化学反应流等典型问题。

Publication:

Y. Liu, J. Lu, and C.-W. Shu, An entropy stable essentially oscillation-free discontinuous Galerkin method for solving ideal magnetohydrodynamic equations, Journal of Computational Physics, v530 (2025), 113911. 

Author:

Yong Liu

State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science and School of Mathematical Science, University of Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China

E-mail addresses: yongliu@lsec.cc.ac.cn

Jianfang Lu

School of Mathematics, South China University of Technology, Canton, Guangdong 510641, People’s Republic of China

Corresponding author.

E-mail addresses: jflu@scut.edu.cn

Chi-Wang Shu

Division of Applied Mathematics, Brown University, Providence, RI 02912, USA

E-mail addresses: chi-wang_shu@brown.edu