A C0 interior penalty method for mth-Laplace equation

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:邱蔚峰(香港城市大学)
:2022-09-26 15:00
:腾讯会议ID:354987414(无密码)

报告人:邱蔚峰(香港城市大学)

时  间:926日下午15:00

地  点:腾讯会议ID354987414(无密码)

内容摘要:

In this talk we will introduce 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 $m$. We can 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.

人简介:

Prof. Weifeng 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.

 

联系人:陈黄鑫