A. Machmoum et D. Esselaoui, Finite element approximation of viscoelastic fluid flow using characteristics method, COMPUT METH, 190(42), 2001, pp. 5603-5618
Citations number
13
Categorie Soggetti
Mechanical Engineering
Journal title
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
It is known that for the numerical approximation of Oldroyd's B model for v
iscoelastic fluid flows some upwinding is needed for the convection of the
extra-stress tensor. In this paper we make the numerical analysis of such a
n approximation with upwinding by the method of characteristics in a finite
element context. The approximate stress, velocity, and pressure are, respe
ctively, P-1 discontinuous, P-2 continuous, and P-1 continuous. We suppose
that the continuous problem admits a sufficiently smooth and sufficiently s
mall solution. We show by a fixed point method that the approximate problem
has a solution and an error bound is given. (C) 2001 Elsevier Science B.V.
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