On a decoupled algorithm
for solving a finite element problem
for the approximation
of viscoelastic fluid flow |
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Authors: | K Najib D Sandri |
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Institution: | (1) Faculté des Sciences, Université Chouaib Doukkali 24000 El Jadida, Maroc , MA;(2) U.A. CNRS-740 LAN, bat. 101, Univ. de Lyon 1, F-69622 Villeurbanne Cedex, France , FR |
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Abstract: | Summary.
The aim of this work is to study a decoupled algorithm of
a fixed point for solving a
finite element (FE) problem for the approximation of viscoelastic
fluid flow obeying an Oldroyd B differential model. The interest for
this algorithm lies in its applications to numerical simulation and
in the cost of computing. Furthermore it is easy to bring this
algorithm into play.
The unknowns
are
the viscoelastic part of the extra stress tensor,
the velocity and
the pressure.
We suppose that the solution
is sufficiently
smooth and small. The approximation
of stress, velocity and pressure are resp.
discontinuous,
continuous,
continuous FE. Upwinding needed for convection of
, is made
by discontinuous FE. The method consists to
solve alternatively a transport equation for the stress,
and a Stokes like problem for velocity and pressure. Previously,
results of existence of the solution for the approximate problem and
error bounds have been obtained using fixed point
techniques with coupled algorithm.
In this paper we show that the mapping of the decoupled
fixed point algorithm is locally (in a neighbourhood of
)
contracting and we obtain existence, unicity (locally) of the solution
of the approximate problem and error bounds.
Received
July 29, 1994 / Revised version received March 13, 1995 |
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Keywords: | Mathematics Subject Classification (1991):65N30 |
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