Inhalt des Dokuments
Preprint 709-2001
Stability and convergence of the two-step BDF for the incompressible Navier-Stokes problem
Author(s) :
Etienne Emmrich
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 709-2001
MSC 2000
- 65M12 Stability and convergence of numerical methods
-
76D05 Navier-Stokes equations
Abstract :
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.
Keywords :
Incompressible Navier-Stokes equation, time discretisation, backward differentiation formula, stability, convergence