Error of the two-step BDF for the incompressible Navier-Stokes problem
ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 5, pp. 757-764.

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.

DOI : 10.1051/m2an:2004037
Classification : 35Q30, 65M12, 76D05
Mots-clés : incompressible Navier-Stokes equation, time discretisation, backward differentiation formula, error estimate, parabolic smoothing 
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     title = {Error of the two-step {BDF} for the incompressible {Navier-Stokes} problem},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
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Emmrich, Etienne. Error of the two-step BDF for the incompressible Navier-Stokes problem. ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 5, pp. 757-764. doi : 10.1051/m2an:2004037. http://archive.numdam.org/articles/10.1051/m2an:2004037/

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