| Issue |
ESAIM: M2AN
Volume 38, Number 5, September-October 2004
|
|
|---|---|---|
| Page(s) | 757 - 764 | |
| DOI | https://doi.org/10.1051/m2an:2004037 | |
| Published online | 15 October 2004 | |
Error of the two-step BDF for the incompressible Navier-Stokes problem
Institut für Mathematik,
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany.
emmrich@math.tu-berlin.de.
Received:
7
October
2003
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.
Mathematics Subject Classification: 35Q30 / 65M12 / 76D05
Key words: Incompressible Navier-Stokes equation / time discretisation / backward differentiation formula / error estimate / parabolic smoothing.
© EDP Sciences, SMAI, 2004
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