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The incompressible Navier-Stokes problem is discretised in time by means of the two-step backward differentiation formula with constant step sizEs. Existence and stability ofa time discrete solution are proved as well as the conve.gence of a piecewise polynomial prolongation towards a weak solution. The results presented cover both the twoand three-dimensional cäse. Furthermore, a linearisation that is based upon a modification ofthe convective term using a second-order extrapolation is considered.

Stability and Convergence of the Two-step BDF for the Incompressible Navier-Stokes Problem