Aleksandra ZimmermannUniversity of Duisburg-Essen

Titre : Convergence of a finite-volume scheme for a heat equation with a multiplicative Lipschitz noise 


Résumé :

We study the approximation by a finite-volume scheme of a heat equation forced by a Lipschitz continuous multiplicative noise in the sense of Itˆo. More precisely, we consider a discretization which is semi-implicit in time and a two-point flux approximation scheme (TPFA) in space. Since the nonlin- earity in the stochastic integral is not compatible with the weak convergence obtained by the a priori estimates, we adapt the method based on the theorem of Prokhorov and on Skorokhod’s representation theorem in order to show stochastically strong convergence of the scheme towards the unique variational solution of our parabolic problem.