A Posteriori Error Analysis for Pressure-Robust HDG Methods for the Stationary Incompressible Navier-Stokes Equations

A hybridizable discontinuous Galerkin method with divergence-free and H(div)-conforming velocity field is considered in this paper for the stationary incompressible Navier-Stokes equations. The pressure-robustness, which means that a priori error estimates for the velocity is independent of the pressure error, is satisfied. As a consequence, an efficient and reliable a posteriori error estimator is proved for the L-2-errors in the velocity gradient and pressure under a smallness assumption. We conclude by several numerical examples which reveal the pressure-robustness and show the performance of the obtained a posteriori error estimator.