An embedded discontinuous Galerkin method for the Oseen equations

Abstract

In this paper, the a prior error estimates of an embedded discontinuous Galerkin method for the Oseen equations are presented. It is proved that the velocity error in the L 2 (Ω) norm, has an optimal error bound with convergence order k + 1, where the constants are dependent on the Reynolds number (or ν − 1 ), in the diffusion-dominated regime, and in the convection-dominated regime, it has a Reynolds-robust error bound with quasi-optimal convergence order k +1 / 2. Here, k is the polynomial order of the velocity space. In addition, we also prove an optimal error estimate for the pressure. Finally, we carry out some numerical experiments to corroborate our analytical results.