The choice of stabilization term is a critical component of the virtual element method (VEM). However, the theory of VEM provides only asymptotic guidance for selecting the stabilization term, which ensures convergence as the mesh size approaches zero, but does not provide a unique prescription for its exact form. Thus, the selection of a suitable stabilization term is often guided by numerical experimentation and analysis of the resulting solution, including factors such as stability, accuracy, and efficiency. In this paper, we establish a new link between VEM and generalized barycentric coordinates, in particular isoparametric finite elements as a specific case. This connection enables the interpretation of the stability as the energy of a particular function in the discrete space, commonly known as the `hourglass mode.' Through this approach, this study sheds light on how the virtual element solution depends on the stabilization term, providing insights into the behavior of the method in more general scenarios.

翻译：稳定化项的选择是虚拟单元法(VEM)中的关键组成部分。然而，VEM的理论仅提供了选择稳定化项的渐进指导，确保随网格尺寸趋近于零时方法的收敛性，但并未对其具体形式给出唯一的规定。因此，合适的稳定化项选择通常需依靠数值实验以及对所得解的分析，包括稳定性、精度和效率等因素。本文建立了VEM与广义重心坐标之间的新联系，特别是将等参有限元视为一种特例。这一联系使得稳定性可被解释为离散空间中特定函数（通常称为"沙漏模式"）的能量。通过这一方法，本研究揭示了虚拟单元解如何依赖于稳定化项，为理解该方法在更一般场景中的行为提供了见解。