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.