The virtual element method (VEM) is a Galerkin approximation method that extends the finite element method to polytopal meshes. In this paper, we present two different conforming virtual element formulations for the numerical approximation of the Stokes problem that work on polygonal meshes.The velocity vector field is approximated in the virtual element spaces of the two formulations, while the pressure variable is approximated through discontinuous polynomials. Both formulations are inf-sup stable and convergent with optimal convergence rates in the $L^2$ and energy norm. We assess the effectiveness of these numerical approximations by investigating their behavior on a representative benchmark problem. The observed convergence rates are in accordance with the theoretical expectations and a weak form of the zero-divergence constraint is satisfied at the machine precision level.

翻译：虚拟元素方法(VEM)是一种Galerkin近似法,它将有限元素方法扩大到多顶层间歇物。在本文中,我们提出了两种不同的匹配虚拟元素配方,用于在多边形模类上起作用的斯托克斯问题的数字近似值。速度矢量场在两种配方的虚拟元素空间中大致可见,而压力变量则通过不连续的多元分子相近。两种配方都处于稳定状态,与2美元和能源标准的最佳趋同率相趋同。我们通过调查它们在具有代表性的基准问题上的行为来评估这些数字近似值的有效性。观察到的趋同率符合理论期望,在机器精确度上满足零振幅限制的薄弱形式。