Analysis of a finite volume element method for the Stokes problem

Details

Serval ID
serval:BIB_17297B478B11
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
Analysis of a finite volume element method for the Stokes problem
Journal
Numerische Mathematik
Author(s)
Quarteroni A., Ruiz-Baier R.
ISSN-L
0029-599X
Publication state
Published
Issued date
2011
Peer-reviewed
Oui
Volume
118
Pages
737-764
Language
english
Abstract
In this paper we propose a stabilized conforming finite
volume element method for the Stokes equations. On
stating the convergence of the method, optimal a priori
error estimates in different norms are obtained by
establishing the adequate connection between the finite
volume and stabilized finite element formulations. A
superconvergence result is also derived by using a
postprocessing projection method. In particular, the
stabilization of the continuous lowest equal order pair
finite volume element discretization is achieved by
enriching the velocity space with local functions that do
not necessarily vanish on the element boundaries.
Finally, some numerical experiments that confirm the
predicted behavior of the method are provided.
Keywords
Stokes problem, multiscale stabilization, finite volume, element method, a priori error estimates, , superconvergence analysis
Create date
02/07/2013 9:54
Last modification date
20/08/2019 12:46
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