An equal-order hybridized discontinuous Galerkin method with a small pressure penalty parameter for the Stokes equations

Abstract

In this paper, an equal-order hybridized discontinuous Galerkin (HDG) method with a small pressure penalty parameter for the Stokes equations is analyzed. When the pressure penalty parameter γ tends to 0 (γ>0), the velocity approximation tends to be H(div)-conforming and exactly divergence-free, and the velocity error bound tends to be pressure-robust. However, taking the value of γ too small will cause the over-stabilization of the pressure. Then, we can provide a post-processing procedure to obtain a stable pressure approximation.