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Error of the two-step BDF for the incompressible Navier-Stokes problem

Published online by Cambridge University Press:  15 October 2004

Etienne Emmrich
Etienne Emmrich*
Affiliation:
Institut für Mathematik, TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany. emmrich@math.tu-berlin.de.
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Abstract

The incompressible Navier-Stokes problem is discretized in time by the two-step backward differentiation formula. Error estimates are proved under feasible assumptions on the regularity of the exact solution avoiding hardly fulfillable compatibility conditions. Whereas the time-weighted velocity error is of optimal second order, the time-weighted error in the pressure is of first order. Suboptimal estimates are shown for a linearisation. The results cover both the two- and three-dimensional case.

Keywords

Incompressible Navier-Stokes equationtime discretisationbackward differentiation formulaerror estimateparabolic smoothing.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 38 , Issue 5 , September 2004 , pp. 757 - 764
Copyright
© EDP Sciences, SMAI, 2004

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