论文标题
关于锁定免费的幽灵惩罚稳定的设计以及与CutFem的关系
On the Design of Locking Free Ghost Penalty Stabilization and the Relation to CutFEM with Discrete Extension
论文作者
论文摘要
在本说明中，我们开发了一种新的稳定机制，用于剪切有限元方法，该方法以两种方式概括了幽灵惩罚类型的先前方法：（1）稳定的数量以及（2）在稳定中连接的元素的选择。特别是，我们可以稳定离散函数的功能，例如有限元元素自由度。随后，我们表明，我们的幽灵惩罚操作员的内核定义了一个有限的元素空间，基于伯曼（Burman）中引入的精神的离散扩展，e。 Hansbo，P。和Larson，M。G.，Cutfem，基于扩展有限元元素空间，Arxiv2101.10052，2021。
In this note, we develop a new stabilization mechanism for cut finite element methods that generalizes previous approaches of ghost penalty type in two ways: (1) The quantity that is stabilized and (2) The choice of elements that are connected in the stabilization. In particular, we can stabilize functionals of the discrete function such as finite element degrees of freedom. We subsequently show that the kernel of our ghost penalty operator defines a finite element space based on discrete extensions in the spirit of those introduced in Burman, E.; Hansbo, P. and Larson, M. G., CutFEM Based on Extended Finite Element Spaces, arXiv2101.10052, 2021.
