Higher-order discontinuous Galerkin time discretizations for the evolutionary Navier–Stokes equations

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 stabilized using a one-level local projection stabilization method. Optimal error bounds for the velocity with constants independent of the viscosity parameter are obtained for both the semidiscrete case and the fully discrete case. Numerical results support the theoretical predictions.