Issue |
ESAIM: M2AN
Volume 35, Number 6, November/December 2001
|
|
---|---|---|
Page(s) | 1007 - 1053 | |
DOI | https://doi.org/10.1051/m2an:2001147 | |
Published online | 15 April 2002 |
Finite-element discretizations of a two-dimensional grade-two fluid model
1
Laboratoire d'Analyse Numérique, Université
Pierre et Marie Curie, 75252 Paris Cedex 05, France.
2
Department of Mathematics, University of
Chicago, Chicago, Illinois 60637-1581, USA.
Received:
5
May
2000
Revised:
3
May
2001
We propose and analyze several finite-element schemes for solving a grade-two fluid model, with a tangential boundary condition, in a two-dimensional polygon. The exact problem is split into a generalized Stokes problem and a transport equation, in such a way that it always has a solution without restriction on the shape of the domain and on the size of the data. The first scheme uses divergence-free discrete velocities and a centered discretization of the transport term, whereas the other schemes use Hood-Taylor discretizations for the velocity and pressure, and either a centered or an upwind discretization of the transport term. One facet of our analysis is that, without restrictions on the data, each scheme has a discrete solution and all discrete solutions converge strongly to solutions of the exact problem. Furthermore, if the domain is convex and the data satisfy certain conditions, each scheme satisfies error inequalities that lead to error estimates.
Mathematics Subject Classification: 65D30 / 65N15 / 65N30
Key words: Mixed formulation / divergence-zero finite elements / inf-sup condition / uniform W1,p-stability / Hood-Taylor method / streamline diffusion.
© EDP Sciences, SMAI, 2001
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.