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Finite element analysis of a simplified stochastic Hookean dumbbells model arising from viscoelastic flows

Published online by Cambridge University Press:  15 November 2006

Andrea Bonito ,
Philippe Clément  and
Marco Picasso
Andrea Bonito
Affiliation:
Institut d'Analyse et Calcul Scientifique, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland. andrea.bonito@a3.epfl.ch; marco.picasso@epfl.ch
Philippe Clément
Affiliation:
Mathematical Institute, Leiden University, P.O. Box 9512, NL-2300 RA Leiden, The Netherlands. PPJEClement@netscape.net
Marco Picasso
Affiliation:
Institut d'Analyse et Calcul Scientifique, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland. andrea.bonito@a3.epfl.ch; marco.picasso@epfl.ch
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Abstract

A simplified stochastic Hookean dumbbells model arising from viscoelastic flows is considered, the convective terms being disregarded. A finite element discretization in space is proposed. Existence of the numerical solution is proved for small data, so as a priori error estimates,using an implicit function theorem and regularity results obtained in [Bonito et al., J. Evol. Equ.6 (2006) 381–398] for the solution of the continuous problem. A posteriori error estimates are also derived.Numerical results with small time steps and a large number of realizations confirm theconvergence rate with respect to the mesh size.

Keywords

ViscoelasticHookean dumbbellsfinite elementsstochastic differential equations.

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Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 40 , Issue 4 , July 2006 , pp. 785 - 814
Copyright
© EDP Sciences, SMAI, 2006

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