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arXiv · 2110.11920

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

Keegan L. A. Kirk·Ayçıl Çeşmelioǧlu·Sander Rhebergen
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Abstract

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

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Keegan L. A. Kirk, Ayçıl Çeşmelioǧlu, Sander Rhebergen. 2021-10-22. Convergence to weak solutions of a space-time hybridized discontinuous Galerkin method for the incompressible Navier--Stokes equations. https://doi.org/10.1090/mcom%2F3780

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