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Main Title: Error of the two-step BDF for the incompressible Navier-Stokes problem
Author(s): Emmrich, Etienne
Type: Research Paper
Abstract: The incompressible Navier-Stokes problem is discretised in time by the two-step backward differentiation formula with constant step sizes. Error estimates are proved under feasible assumptions on the regularity of the exact solution. The question of compatibility of problem data is taken into account. Whereas the time-weighted velocity error is of optimal second order in the $l^{\infty}(L^2)$- and $l^2(H_0^1)$-norm, the time-weighted error in the pressure is of first order in the $l^{\infty}(L^2/\mathbbm{R})$-norm. Furthermore, a linearisation that is based upon a modification of the convective term using a formally second-order extrapolation is considered. The velocity error is then shown to be of order $3/2$, and the pressure error is of order $1/2$. The results presented cover both the two- and three-dimensional case. Particular attention is directed to appearing constants and step size restrictions.
Subject(s): incompressible Navier-Stokes equation
time discretisation
backward differentiation formula
error estimate
parabolic smoothing
Issue Date: 1-Aug-2002
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 65M12 Stability and convergence of numerical methods
76D05 Navier-Stokes equations
35Q30 Stokes and Navier-Stokes equations
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2002, 741
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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