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arXiv · 2103.13492

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

Keegan L. A. Kirk·Tamás L. Horváth·Sander Rhebergen
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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 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.

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Keegan L. A. Kirk, Tamás L. Horváth, Sander Rhebergen. 2021-03-24. Analysis of an exactly mass conserving space-time hybridized discontinuous Galerkin method for the time-dependent Navier--Stokes equations. https://doi.org/10.1090/mcom/3796

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