Error of the two-step BDF for the incompressible Navier-Stokes problem
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 5, p. 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 : https://doi.org/10.1051/m2an:2004037
Classification:  35Q30,  65M12,  76D05
Keywords: incompressible Navier-Stokes equation, time discretisation, backward differentiation formula, error estimate, parabolic smoothing
@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},
     publisher = {EDP-Sciences},
     volume = {38},
     number = {5},
     year = {2004},
     pages = {757-764},
     doi = {10.1051/m2an:2004037},
     zbl = {1076.76054},
     mrnumber = {2104427},
     language = {en},
     url = {http://www.numdam.org/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, Volume 38 (2004) no. 5, pp. 757-764. doi : 10.1051/m2an:2004037. http://www.numdam.org/item/M2AN_2004__38_5_757_0/

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