Analysis of Pressure-Robust Embedded-Hybridized Discontinuous Galerkin Methods for the Stokes Problem Under Minimal Regularity

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.