We present a stability analysis of the Discontinuous Galerkin method on polygonal and polyhedral meshes (PolyDG) for the Stokes problem. In particular, we analyze the discrete inf-sup condition for different choices of the polynomial approximation order of the velocity and pressure approximation spaces. To this aim, we employ a generalized inf-sup condition with a pressure stabilization term. We also prove a priori hp-version error estimates in suitable norms. We numerically check the behaviour of the inf-sup constant and the order of convergence with respect to the mesh configuration, the mesh-size, and the polynomial degree. Finally, as a relevant application of our analysis, we consider the PolyDG approximation for a fluid-structure interaction problem and we numerically explore the stability properties of the method.

翻译：我们提出对多角和多面介质(PollyDG)的不连续加勒金方法(PollyDG)的稳定性分析, 特别是分析对速度和压力近似空间多面近似顺序的不同选择的离散内位条件。 为此, 我们使用一个具有压力稳定期的普通内位条件。 我们还证明在适当的规范中有一个先验性动误差估计。 我们用数字检查内向常数的行为以及网目配置、网目尺寸和多面度的趋同顺序。 最后, 作为我们分析的相关应用, 我们考虑将多面方位近似作为流体结构相互作用问题的一种相关应用, 我们用数字来探索该方法的稳定性。