We introduce and analyze a space-time hybridized discontinuous Galerkin method for the evolutionary Navier--Stokes equations. Key features of the numerical scheme include point-wise mass conservation, energy stability, and pressure robustness. We prove that there exists a solution to the resulting nonlinear algebraic system in two and three spatial dimensions, and that this solution is unique in two spatial dimensions under a small data assumption. A priori error estimates are derived for the velocity in a mesh-dependent energy norm.

翻译：我们为进化导航-斯托克斯方程式引入并分析一种时空混合不连续的Galerkin方法。该数字方法的关键特征包括点巧质量节能、能源稳定性和压力稳健性。我们证明,由此产生的非线性代数系统在两个和三个空间维度上存在解决办法,根据一个小的数据假设,这一解决办法在两个空间维度上是独一无二的。对于网状依赖能源规范中的速度,可以得出先验误差估计数。