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Existence, a priori and a posteriori error estimates for a nonlinear three-field problem arising from Oldroyd-B viscoelastic flows

Published online by Cambridge University Press:  15 April 2002

Marco Picasso  and
Jacques Rappaz
Marco Picasso
Affiliation:
Département de Mathématiques, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland.
Jacques Rappaz
Affiliation:
Département de Mathématiques, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland.
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Abstract

In this paper, a nonlinear problem corresponding to a simplified Oldroyd-B model without convective terms is considered. Assuming the domain to be a convex polygon, existence of a solution is proved for small relaxation times. Continuous piecewise linear finite elements together with a Galerkin Least Square (GLS) method are studied for solving this problem. Existence and a priori error estimates are established using a Newton-chord fixed point theorem, a posteriori error estimates are also derived. An Elastic Viscous Split Stress (EVSS) scheme related to the GLS method is introduced. Numerical results confirm the theoretical predictions.

Keywords

Viscoelastic fluidsGalerkin Least Square finite elements.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 , Issue 5 , September 2001 , pp. 879 - 897
Copyright
© EDP Sciences, SMAI, 2001

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