哈尔滨工业大学（深圳）学术讲座

演讲人Speaker：   香港城市大学 邱蔚峰  教授

题目Title: A C^0 Interior Penalty Method for $m$th-Laplace Equation

时间Date：2023年 11 月 20 日       Time：14:00–15:00

地点Venue：腾讯会议 442-674-646

链接：https://meeting.tencent.com/dm/yX3CXNLw0riO

内容摘要Abstract： 

In this paper, we propose a $C^0$ interior penalty method for $m$th-Laplace equation on bounded Lipschitz polyhedral domain in $\mathbb{R}^d$, where $m$ and $d$ can be any positive integers. The standard $H^1$-conforming piecewise $r$-th order polynomial space is used to approximate the exact solution $u$, where $r$ can be any integer greater than or equal to $m$. Unlike the interior penalty method in Gudi and Neilan [IMA J. Numer. Anal. 31 (2011) 1734–1753], we avoid computing $D^m$ of numerical solution on each element and high order normal derivatives of numerical solution along mesh interfaces. Therefore our method can be easily implemented. After proving discrete $H^m$-norm bounded by the natural energy semi-norm associated with our method, we manage to obtain stability and optimal convergence with respect to discrete $H^m$-norm. The error estimate under the low regularity assumption of the exact solution is also obtained. Numerical experiments validate our theoretical estimate.

个人简介(About the speaker):

Prof. Frederick Qiu received his BSc from Shanghai Normal University in 2000, Master from University of Alabama in Huntsville in 2006, and PhD from the University of Texas at Austin in 2010. His PhD advisor is Professor Leszek Demkowicz. Before joining City University in 2012, he worked as a Postdoctoral Fellow at IMA (Institute for Mathematics and Its Applications), University of Minnesota. His postdoctoral mentor is Professor Bernardo Cockburn. His major research interests include scientific computing and numerical analysis for PDE.