Convergence to weak solutions of a space-time hybridized discontinuous Galerkin method for the incompressible Navier–Stokes equations

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