Finite element analysis of a simplified stochastic Hookean dumbbells model arising from viscoelastic flows
Institut d'Analyse et Calcul Scientifique,
École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland. email@example.com; firstname.lastname@example.org
2 Mathematical Institute, Leiden University, P.O. Box 9512, NL-2300 RA Leiden, The Netherlands. PPJEClement@netscape.net
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