论文标题
尖锐的Korn对分段$ H^1 $空间及其应用的不平等
A sharp Korn's inequality for piecewise $H^1$ space and its application
论文作者
论文摘要
在本文中，我们基于域的一般多边形或多面体分解，重新查看了Korn对分段$ h^1 $空间的不平等。我们的Korn的不平等表达了最小的跳跃项。通过表征将刚体模式限制到分区边缘/面的限制来确定这些最小的跳跃项。这种最小的跳跃条件也表明可以达到Korn的不平等。我们的结果的清晰度和明确给定的最小条件可以用于测试任何给定的有限元空间是否满足Korn的不平等，并立即构建或修改不合格的有限元素，以使Korn的不平等持有。
In this paper, we revisit Korn's inequality for the piecewise $H^1$ space based on general polygonal or polyhedral decompositions of the domain. Our Korn's inequality is expressed with minimal jump terms. These minimal jump terms are identified by characterizing the restriction of rigid body mode to edge/face of the partitions. Such minimal jump conditions are shown to be sharp for achieving the Korn's inequality as well. The sharpness of our result and explicitly given minimal conditions can be used to test whether any given finite element spaces satisfy Korn's inequality, immediately as well as to build or modify nonconforming finite elements for Korn's inequality to hold.
