In this talk, we will discuss low Weissenberg number
effects on mathematical properties of solutions for several PDEs
governing different viscoelastic fluids.
This talk is based on a joint work with Céline Labart. We are interested in this paper in the numerical simulation of solutions to Backward Stochastic Differential Equations. There are several existing methods to handle this problem and one of the main difficulty is always to compute conditional expectations.
Even though our approach can also be applied in the case of the dynamic programmation equation, our starting point is the use of Picard's iterations that we write in a forward way
In order to compute the conditional expectations, we use Wiener Chaos expansions of the underlying random variables. From a practical point of view, we keep only a finite number of terms in the expansions and we get explicit formulas.
We will present numerical experiments and results on the error analysis.