Analysis of pressure-robust embedded-hybridized discontinuous Galerkin methods for the Stokes problem under minimal regularity

Abstract

We present analysis of two lowest-order hybridizable discontinuous Galerkin methods for the Stokes problem, while making only minimal regularity assumptions on the exact solution. The methods under consideration have previously been shown to produce H(div)-conforming and divergence-free approximate velocities. Using these properties, we derive a priori error estimates for the velocity that are independent of the pressure. These error estimates, which assume only H 1+s -regularity of the exact velocity fields for any s ∈ [0, 1], are optimal in a discrete energy norm. Error estimates for the velocity and pressure in the L 2 -norm are also derived in this minimal regularity setting. Our theoretical findings are supported by numerical computations.

A New Global Divergence Free and Pressure-Robust HDG Method for Tangential Boundary Control of Stokes Equations

“…They obtained pressure-robust scheme for the Navier-Stokes equation. For other pressure-robust HDG methods, see [18,19,20,21,22]. In this paper, we propose a new HDG scheme with less degrees of freedom than that of [16], apply it to a tangential boundary control problem governed by the Stokes equation, and prove that the method is pressure-robust.…”