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.
翻译：在本说明中,我们为削减有限要素的方法制定了一个新的稳定机制,以两种方式概括以往的幽灵惩罚类型做法:(1) 稳定数量和(2) 与稳定相关的要素的选择,特别是,我们可以稳定离散功能的功能,例如自由的有限要素度,随后我们表明,我们的幽灵惩罚操作员的内核本着Burman, E.;Hansbo, P.和Larson, M. G., CutFEM 以扩展的金融元素空间为基础,根据在Burman, E.;Hansbo, P.和Larson, M. G., CutFEM 中引入的那些精神,根据离散扩展的扩展元素空间, arXiv 2101110052, 2021。
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