The virtual element method was introduced 10 years ago and it has generated a large number of theoretical results and applications ever since. Here, we overview the main mathematical results concerning the stabilization term of the method as an introduction for newcomers in the field. In particular, we summarize the proofs of some results for two dimensional ``nodal'' conforming and nonconforming virtual element spaces to pinpoint the essential tools used in the stability analysis. We discuss their extensions to several other virtual elements. Finally, we show several ways to prove interpolation estimates, including a recent one that is based on employing the stability bounds.

翻译：虚拟单元法于十年前提出，自此产生了大量理论成果与应用。本文作为该领域新入门者的导引，概述了关于该方法稳定化项的主要数学结论。具体而言，我们总结了二维“节点型”协调与非协调虚拟单元空间中若干结果的证明过程，以阐明稳定性分析中使用的核心工具。我们讨论了这些结果向其他多种虚拟单元的推广。最后，展示了证明插值估计的若干途径，包括一种基于稳定性界的新近方法。