| Issue |
ESAIM: M2AN
Volume 40, Number 4, July-August 2006
|
|
|---|---|---|
| Page(s) | 785 - 814 | |
| DOI | https://doi.org/10.1051/m2an:2006030 | |
| Published online | 15 November 2006 | |
Finite element analysis of a simplified stochastic Hookean dumbbells model arising from viscoelastic flows
1
Institut d'Analyse et Calcul Scientifique,
École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland. andrea.bonito@a3.epfl.ch; marco.picasso@epfl.ch
2
Mathematical Institute, Leiden University, P.O. Box 9512, NL-2300 RA Leiden,
The Netherlands. PPJEClement@netscape.net
Received:
2
December
2005
Revised:
1
May
2006
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 the convergence rate with respect to the mesh size.
Mathematics Subject Classification: 46T / 65M / 76A
Key words: Viscoelastic / Hookean dumbbells / finite elements / stochastic differential equations.
© EDP Sciences, SMAI, 2006
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