IJPAM: Volume 21, No. 4 (2005)

NUMERICAL ANALYSIS OF STABILIZED METHOD
FOR TRANSIENT VISCOELASTIC FLOWS

Mohammed Bensaada$^{1}$, Driss Esselaoui$^2$
$^{1,2}$Laboratoire of Engineering Sciences
Numerical Analysis and Optimisation(SIANO)
Faculty of Sciences
niversity Ibn Tofail
B.P. 133, KENITRA, MAROCCO
e-mail: mk_bensaada@yahoo.fr
e-mail: desselaoui@yahoo.fr


Abstract.We study a new approximation scheme of transient viscoelastic fluid flow obeying an Oldroyd-B type constitutive equation. The stress, velocity and pressure are approximated by, respectively $P_{1}-$continuous, $P_{2}-$
continuous, $P_{1}-$continuous. The new stabilized formulation bases on the choice of a modified Euler method connected to the streamline upwinding Petrov-Galerkin(SUPG) method (cf. Bensaada et al [#!BE!#]). In this method, the standard Euler-SUPG formulation is modified in order to introduce some upwinding and to stabilize the tensoriel transport term of the Oldroyd derivative. The continuous problem is supposed to admit a sufficiently smooth and sufficiently small solution. We show that the approximate problem has a solution and we give an error bound.

Received: May 23, 2005

AMS Subject Classification: 65N12, 65N15, 65N30, 76A10

Key Words and Phrases: transient viscoelastic flows, finite elements, stabilized method, modified Euler-SUPG method

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 21
Issue: 4