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Stability and convergence of the two-step BDF for the incompressible Navier-Stokes problem

Emmrich, Etienne

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

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 of a time discrete solution is proved as well as the convergence of a piecewise polynomial prolongation towards a weak solution. The results presented cover both the two- and three-dimensional case. Furthermore, a linearisation that is based upon a modification of the convective term using a second-order extrapolation is considered.