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 $H(\text{div})$-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 $s\in [0,1]$, 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.

Cited by in corpus (1)

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