We prove that a space-time hybridized discontinuous Galerkin method for the evolutionary Navier--Stokes equations converges to a weak solution as the time step and mesh size tend to zero. Moreover, we show that this weak solution satisfies the energy inequality. To perform our analysis, we make use of discrete functional analysis tools and a discrete version of the Aubin--Lions--Simon theorem.

翻译：我们证明进化纳维埃-斯托克斯方程式的时空混合不连续的Galerkin方法与一个薄弱的解决方案相融合,因为时间步骤和网目尺寸一般为零。此外,我们证明这一薄弱的解决方案满足了能源不平等。为了进行分析,我们使用了离散功能分析工具和离散版本的Aubin-Lion-Simon定理。