报告人：张智民（韦恩州立大学）

报告时间：2025年5月10日（星期六）16:00-18:00    

报告地点：科技楼南楼702会议室  

报告摘要：Optimal convergence rate of the $P^k$ discontinuous Galerkin (DG) methods under the rectangular mesh for hyperbolic equations is a long-standing unsolved theoretical problem. Until today, the best result is $h+1/2$ for general rectangular meshes. In 2020, Liu, Shu, and Zhang proved that under a uniform rectangular mesh, the optimal convergence rate is $k+1$ for linear problems with constant coefficients. For non-constant coefficients, the optimal rate has been proved for $k=0,1,2,3$. For the nonlinear case, only $k=2,3$ have been proved. In this work, we prove the $k+1$ optimal rate of convergence under the uniform rectangular mesh for variable coefficients and nonlinear cases for all $k$. In addition, we discover some super-convergence phenomena for $P^k$-DG for the first time.

报告人简介：张智民，美国韦恩州立大学教授，Charles H. Gershenson 杰出学者。研究方向是偏微分方程数值解，包括有限元，有限体积，谱方法等，发表学术论文200余篇；提出的多项式保持重构Polynomial Preserving Recovery（PPR）格式于2008年被国际上广为流行的大型商业软件 COMSOL Multiphysics 采用，并使用至今。担任或曾任“Mathematics of Computation” “Journal of Scientific Computing” 等9个国际计算数学杂志编委。

邀请人：李东方