Convergence of a finite-volume scheme for a heat equation with a multiplicative Lipschitz noise
Résumé
We study here the approximation by a finite-volume scheme of a heat equation forced by a Lipschitz continuous multiplicative noise in the sense of Itô. More precisely, we consider a discretization which is semi-implicit in time and a two-point flux approximation scheme (TPFA) in space. We adapt the method based on the theorem
of Prokhorov to obtain a convergence in distribution result, then Skorokhod's
representation theorem yields the convergence of the scheme towards a martingale
solution and the Gyöngy-Krylov argument is used to prove convergence in probability
of the scheme towards the unique variational solution of our parabolic problem.
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