Finite element approximation of viscoelastic fluid flow using characteristics method

Citation
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
ISSN journal
00457825 → ACNP
Volume
190
Issue
42
Year of publication
2001
Pages
5603 - 5618
Database
ISI
SICI code
0045-7825(2001)190:42<5603:FEAOVF>2.0.ZU;2-C
Abstract
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. All rights reserved.