Analysis of a pressure-robust hybridized discontinuous Galerkin method for the stationary Navier-Stokes equations

Abstract

We present well-posedness and an a priori error analysis of the hybridized discontinuous Galerkin method for the stationary form of the Navier-Stokes problem proposed in (J Sci Comput, 76(3):1484{ 1501, 2018). This scheme was shown to result in an approximate velocity eld that is pointwise divergence-free and divergence-conforming. As a consequence we show that the velocity error estimate is independent of the pressure. Furthermore, we show that estimates for both the velocity and pressure are optimal. Numerical examples demonstrate pressure-robustness and optimality of the scheme.