Low Regularity Error Analysis for an H(div)-conforming Discontinuous Galerkin Approximation of Stokes Problem

In this paper, we derive an improved error estimate for the H(div)-conforming discontinuous Galerkin (DG) approximation of the Stokes equations, assuming only minimal regularity on the exact solution. The estimate relies on both a priori and a posteriori analysis, and thus is called a medius error analysis. More precisely, we proved an optimal order error estimate under the assumption ( u, p ) ∈ H 1 + s ( Ω ) × H s ( Ω ) with any s ∈ ( 0, 1 ]. Extension to the standard interior penalty DG methods is also explored. Finally, numerical results are provided to verify our theoretical findings.