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

Kirk, Keegan; Horváth, Tamás; Rhebergen, Sander

doi:10.1090/mcom/3796

Analysis of an exactly mass conserving space-time hybridized discontinuous Galerkin method for the time-dependent Navier–Stokes equations
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by Keegan L. A. Kirk, Tamás L. Horváth and Sander Rhebergen HTML | PDF

Math. Comp. 92 (2023), 525-556 Request permission

Abstract:

We introduce and analyze a space-time hybridized discontinuous Galerkin method for the evolutionary Navier–Stokes equations. Key features of the numerical scheme include pointwise 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.

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