We numerically investigate the possibility of defining stabilization-free Virtual Element (VEM) discretizations of advection-diffusion problems in the advection-dominated regime. To this end, we consider a SUPG stabilized formulation of the scheme. Numerical tests comparing the proposed method with standard VEM show that the lack of an additional arbitrary stabilization term, typical of VEM schemes, that adds artificial diffusion to the discrete solution, allows to better approximate boundary layers, in particular in the case of a low order scheme.

翻译：本文数值探究了在对流主导状态下定义无稳定化虚拟元法（VEM）离散化对流扩散问题的可能性。为此，我们引入该格式的SUPG稳定化形式。数值实验将所提方法与标准VEM进行对比，结果表明：摒弃VEM格式中典型添加人工扩散至离散解的额外任意稳定化项，能够更好地逼近边界层，尤其在低阶格式情形下效果显著。