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