Emmrich, Etienne2021-12-172021-12-172001-02-012197-8085https://depositonce.tu-berlin.de/handle/11303/15978http://dx.doi.org/10.14279/depositonce-14751The 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.en510 Mathematikincompressible Navier-Stokes equationtime discretisationbackward differentiation formulastabilityconvergenceResearch Paper