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Preprint 709-2001

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

Source file is available as :   Postscript Document

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

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