Please use this identifier to cite or link to this item: http://dx.doi.org/10.14279/depositonce-14236
 Main Title: Error of the two-step BDF for the incompressible Navier-Stokes problem Author(s): Emmrich, Etienne Type: Research Paper URI: https://depositonce.tu-berlin.de/handle/11303/15463http://dx.doi.org/10.14279/depositonce-14236 License: http://rightsstatements.org/vocab/InC/1.0/ 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 equationtime discretisationbackward differentiation formulaerror estimateparabolic 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 methods76D05 Navier-Stokes equations35Q30 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