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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.
@article{M2AN_2004__38_5_757_0,
author = {Emmrich, Etienne},
title = {Error of the two-step {BDF} for the incompressible {Navier-Stokes} problem},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {757--764},
publisher = {EDP-Sciences},
volume = {38},
number = {5},
year = {2004},
doi = {10.1051/m2an:2004037},
mrnumber = {2104427},
zbl = {1076.76054},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2004037/}
}
TY - JOUR AU - Emmrich, Etienne TI - Error of the two-step BDF for the incompressible Navier-Stokes problem JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2004 SP - 757 EP - 764 VL - 38 IS - 5 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2004037/ DO - 10.1051/m2an:2004037 LA - en ID - M2AN_2004__38_5_757_0 ER -
%0 Journal Article %A Emmrich, Etienne %T Error of the two-step BDF for the incompressible Navier-Stokes problem %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2004 %P 757-764 %V 38 %N 5 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2004037/ %R 10.1051/m2an:2004037 %G en %F M2AN_2004__38_5_757_0
Emmrich, Etienne. Error of the two-step BDF for the incompressible Navier-Stokes problem. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 38 (2004) no. 5, pp. 757-764. doi: 10.1051/m2an:2004037
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