Analysis of an exactly mass conserving space-time hybridized discontinuous Galerkin method for the time-dependent Navier--Stokes equations
Numerical Analysis
2023-07-07 v2 Numerical Analysis
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.
Keywords
Cite
@article{arxiv.2103.13492,
title = {Analysis of an exactly mass conserving space-time hybridized discontinuous Galerkin method for the time-dependent Navier--Stokes equations},
author = {Keegan L. A. Kirk and Tamás L. Horváth and Sander Rhebergen},
journal= {arXiv preprint arXiv:2103.13492},
year = {2023}
}