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

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.

References in corpus (1)

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

Cited by in corpus (1)

• A note on the compactness properties of discontinuous Galerkin time discretizations