Analysis of an Embedded-Hybridized Discontinuous Galerkin Method for the Time-Dependent Incompressible Navier–Stokes Equations

In this paper, the a prior error estimates of an embedded-hybridized discontinuous Galerkin method for the time-dependent Navier–Stokes equations are presented. It is proved that the velocity error in the L^2(Ω ) norm, where the constants are independent of the Reynolds number Re (or ν ^-1 ), is quasi-optimal with pre-asymptotic convergence order of k+1/2 in case of ν≤ Ch ‖u‖ _L^∞(L^∞(Ω )) , with k the polynomial order of the velocity space. In addition, we also provide a Reynolds-dependent error bound with asymptotic convergence order of k+1 for the case of the low mesh Reynolds number Re_h , which is denoted as h ‖u‖ _L^∞(L^∞(Ω ))/ν . Finally, numerical experiments are carried out to confirm the rates of convergence.