Higher-order discontinuous Galerkin time discretizations the\n evolutionary Navier--Stokes equations

Discontinuous Galerkin methods of higher order are applied as temporal\ndiscretizations for the transient Navier--Stokes equations. The spatial\ndiscretization based on inf-sup stable pairs of finite element spaces is\nstabilised using a one-level local projection stabilisation method. Optimal\nerror bounds for the velocity with constants independent of the viscosity\nparameter are obtained for the semi-discrete case. For the fully discrete case,\nerror estimates for both velocity and pressure are given. Numerical results\nsupport the theoretical predictions.\n