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The choice of stabilization term is a critical component of the virtualelement method (VEM). However, the theory of VEM provides only asymptoticguidance for selecting the stabilization term, which ensures convergence as themesh size approaches zero, but does not provide a unique prescription for itsexact form. Thus, the selection of a suitable stabilization term is oftenguided 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, inparticular isoparametric finite elements as a specific case. This connectionenables the interpretation of the stability as the energy of a particularfunction in the discrete space, commonly known as the `hourglass mode.' Throughthis approach, this study sheds light on how the virtual element solutiondepends on the stabilization term, providing insights into the behavior of themethod in more general scenarios.

Quantitative study of the stabilization parameter in the virtual element method