In this paper, we extend our work for the heat equation in [4] and for the Stokes equations
in [5] to the nonstationary Navier-Stokes equations in two dimensions. We examine continu-
ous Galerkin-Petrov (cGP) time discretization schemes for nonstationary incompressible flow.
In particular, we implement and analyze numerically the higher order cGP(2)-method. For
the space discretization, we use the LBB-stable finite element pair Q2=Pdisc
1 . The discretized
systems of nonlinear equations are treated by using the fixed-point as well as the Newton
method and the associated linear subproblems are solved by using a monolithic multigrid
solver with GMRES method as smoother. We perform nonstationary simulations for a benchmarking
configuration to analyze the temporal accuracy and efficiency of the presented time
discretization scheme.