应兰州大学数学与统计学院和甘肃省计算数学基础学科研究中心邀请,武汉大学李勇霖教授将于2026年04月13日下午作学术报告，欢迎全校师生参加。

报告题目：Higher-order FEM and CIP-FEM for Helmholtz equation with high wave number and perfectly matched layer truncation

时间：2026年04月13日(星期一) 下午 14:30

地点：理工楼631报告厅

报告摘要：The Helmholtz equation with high wave number on the entire space is truncated into a bounded domain using the perfectly matched layer (PML) technique and subsequently discretized by the higher-order finite element method (FEM) and the continuous interior penalty finite element method (CIP-FEM). By formulating an elliptic problem involving a linear combination of a finite number of eigenfunctions related to the PML differential operator, a wave-number-explicit decomposition lemma is proved for the PML problem, which implies that the PML solution can be decomposed into a non-oscillating elliptic part and an oscillating but piecewise smooth part. The preasymptotic error estimates in the energy norm for both the p-th order CIP-FEM and FEM are proved to be C1(kh)p + C2k(kh)2p + C3EPML under the mesh condition that k2p+1h2p is sufficiently small, where k is the wave number, h is the mesh size, and EPML is the PML truncation error which is exponentially small. Numerical experiments are presented to validate the theoretical findings, illustrating that the higher-order CIP-FEM can greatly reduce the pollution errors by selecting appropriate penalty parameters.

欢迎广大师生参加！

报告人简介

李勇霖, 2024年9月加入武汉大学数学与统计学院, 现为武汉大学教授、博导。2019年6月于南京大学数学系获得计算数学博士学位, 随后先后于中国科学院数学与系统科学研究院以及香港理工大学应用数学系从事博士后研究。研究方向为偏微分方程数值解法, 尤其是散射问题的有限元理论分析与快速计算。主要成果发表在《SIAM J. Numer. Anal.》《IMA J. Numer. Anal.》和《J. Comput. Phys.》等高水平期刊. 2024年入选湖北省“楚天学子”。 目前主持一项国家优秀青年科学基金项目(海外)以及青年科学基金项目(C类)。

甘肃省计算数学基础学科研究中心

数学与统计学院

萃英学院

2026年4月9日