# Error of the two-step BDF for the incompressible Navier-Stokes problem

- Volume: 38, Issue: 5, page 757-764
- ISSN: 0764-583X

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topEmmrich, Etienne. "Error of the two-step BDF for the incompressible Navier-Stokes problem." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 38.5 (2004): 757-764. <http://eudml.org/doc/244827>.

@article{Emmrich2004,

abstract = {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.},

author = {Emmrich, Etienne},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {incompressible Navier-Stokes equation; time discretisation; backward differentiation formula; error estimate; parabolic smoothing; two-step backward differentiation formula; time-weigted error},

language = {eng},

number = {5},

pages = {757-764},

publisher = {EDP-Sciences},

title = {Error of the two-step BDF for the incompressible Navier-Stokes problem},

url = {http://eudml.org/doc/244827},

volume = {38},

year = {2004},

}

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 - Modélisation Mathématique et Analyse Numérique

PY - 2004

PB - EDP-Sciences

VL - 38

IS - 5

SP - 757

EP - 764

AB - 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.

LA - eng

KW - incompressible Navier-Stokes equation; time discretisation; backward differentiation formula; error estimate; parabolic smoothing; two-step backward differentiation formula; time-weigted error

UR - http://eudml.org/doc/244827

ER -

## References

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- [2] E. Emmrich, Analysis von Zeitdiskretisierungen des inkompressiblen Navier-Stokes-Problems. Cuvillier, Göttingen (2001). Zbl0982.76003
- [3] E. Emmrich, Error of the two-step BDF for the incompressible Navier-Stokes problem. Preprint 741, TU Berlin (2002). Zbl1076.76054
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- [7] S. Müller-Urbaniak, Eine Analyse des Zwischenschritt-$\theta $-Verfahrens zur Lösung der instationären Navier-Stokes-Gleichungen. Preprint 94-01 (SFB 359), Univ. Heidelberg (1994). Zbl0796.76072
- [8] A. Prohl, Projection and Quasi-compressibility Methods for Solving the Incompressible Navier-Stokes Equations. Teubner, Stuttgart (1997). Zbl0874.76002MR1472237
- [9] R. Temam, Navier-Stokes Equations. Theory and Numerical Analysis. North-Holland Publ. Company, Amsterdam (1977). Zbl0383.35057MR609732
- [10] R. Temam, Navier-Stokes Equations and Nonlinear Functional Analysis. CBMS-NSF Reg. Confer. Ser. Appl. Math. SIAM 41 (1985). Zbl0833.35110MR764933

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