Numerical analysis of micro-macro simulations of polymeric fluid flows: A simple case

We present in this paper the numerical analysis of a simple micro-macro simulation of a polymeric fluid flow, namely the shear flow for the Hookean dumbbells model. Although restricted to this academic case (which is however used in practice as a test problem for new numerical strategies to be applied to more sophisticated cases), our study can be considered as a first step towards that of more complicated models. Our main result states the convergence of the fully discretized scheme (finite element in space, finite difference in time, plus Monte Carlo realizations) towards the coupled solution of a partial differential equation/stochastic differential equation system.