In an earlier paper, we had performed numerical comparisons for different time stepping
schemes for the incompressible Navier-Stokes equations. In this paper, we present the
numerical analysis in the context of the Navier-Stokes equations for a new time-stepping
theta-scheme which has been recently proposed by Glowinski. Like
the well-known classical Fractional-Step-theta-scheme which had been introduced by
Glowinski, too, and which is still one of the most popular
time stepping schemes, with or without operator splitting techniques, this new scheme
consists of 3 substeps with non-equidistant substepping to build one macro time step.
However, in contrast to the Fractional-Step-theta-scheme, the second substep can be
formulated as an extrapolation step for previously computed data only, and the two
remaining substeps look like a Backward Euler step so