Discontinuous Galerkin methods of higher order are applied as temporal discretizations for the transientNavier–Stokes equations. The spatial discretization based on inf–sup stable pairs of finite element spacesis stabilized using a one-level local projection stabilization method. Optimal error bounds for the velocitywith constants independent of the viscosity parameter are obtained for both the semidiscrete case and thefully discrete case. Numerical results support the theoretical predictions.