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

dc.contributor.authorEmmrich, Etienne
dc.date.accessioned2021-12-17T10:05:14Z
dc.date.available2021-12-17T10:05:14Z
dc.date.issued2002-08-01
dc.description.abstractThe 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.issn2197-8085
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/15463
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-14236
dc.language.isoenen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.ddc510 Mathematiken
dc.subject.otherincompressible Navier-Stokes equationen
dc.subject.othertime discretisationen
dc.subject.otherbackward differentiation formulaen
dc.subject.othererror estimateen
dc.subject.otherparabolic smoothingen
dc.titleError of the two-step BDF for the incompressible Navier-Stokes problemen
dc.typeResearch Paperen
dc.type.versionsubmittedVersionen
tub.accessrights.dnbfreeen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften>Inst. Mathematikde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
tub.series.issuenumber2002, 741en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.subject.msc200065M12 Stability and convergence of numerical methodsen
tub.subject.msc200076D05 Navier-Stokes equationsen
tub.subject.msc200035Q30 Stokes and Navier-Stokes equationsen
Files
Original bundle
Now showing 1 - 1 of 1
Loading…
Thumbnail Image
Name:
art2.pdf
Size:
229.17 KB
Format:
Adobe Portable Document Format
Description:
Collections