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

 dc.contributor.author Emmrich, Etienne dc.date.accessioned 2021-12-17T10:05:14Z dc.date.available 2021-12-17T10:05:14Z dc.date.issued 2002-08-01 dc.description.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. en dc.identifier.issn 2197-8085 dc.identifier.uri https://depositonce.tu-berlin.de/handle/11303/15463 dc.identifier.uri http://dx.doi.org/10.14279/depositonce-14236 dc.language.iso en en dc.rights.uri http://rightsstatements.org/vocab/InC/1.0/ en dc.subject.ddc 510 Mathematik en dc.subject.other incompressible Navier-Stokes equation en dc.subject.other time discretisation en dc.subject.other backward differentiation formula en dc.subject.other error estimate en dc.subject.other parabolic smoothing en dc.title Error of the two-step BDF for the incompressible Navier-Stokes problem en dc.type Research Paper en dc.type.version submittedVersion en tub.accessrights.dnb free en tub.affiliation Fak. 2 Mathematik und Naturwissenschaften>Inst. Mathematik de tub.affiliation.faculty Fak. 2 Mathematik und Naturwissenschaften de tub.affiliation.institute Inst. Mathematik de tub.publisher.universityorinstitution Technische Universität Berlin en tub.series.issuenumber 2002, 741 en tub.series.name Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin en tub.subject.msc2000 65M12 Stability and convergence of numerical methods en tub.subject.msc2000 76D05 Navier-Stokes equations en tub.subject.msc2000 35Q30 Stokes and Navier-Stokes equations en
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