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

Bonito, Andrea; Clément, Philippe; Picasso, Marco

ESAIM: Modélisation mathématique et analyse numérique, Tome 40 (2006) no. 4, pp. 785-814.

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.

Classification : 46T, 65M, 76A
Mots clés : viscoelastic, hookean dumbbells, finite elements, stochastic differential equations

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