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 - Mod\'elisation Math\'ematique et Analyse Num\'erique}, volume = {38}, year = {2004}, pages = {757-764}, doi = {10.1051/m2an:2004037}, mrnumber = {2104427}, zbl = {1076.76054}, language = {en}, url = {http://dml.mathdoc.fr/item/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 - Modélisation Mathématique et Analyse Numérique, Tome 38 (2004) pp. 757-764. doi : 10.1051/m2an:2004037. http://gdmltest.u-ga.fr/item/M2AN_2004__38_5_757_0/
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