Analysis of an exactly mass conserving space-time hybridized discontinuous Galerkin method for the time-dependent Navier–Stokes equations

03/24/2021

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by   Keegan L. A. Kirk, et al.

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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 both the velocity and pressure.