Convergence of a finite-volume scheme for a heat equation with a multiplicative stochastic force

Caroline Bauzet (1) , Flore Nabet (2)

1 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

We present here the discretization by a finite-volume scheme of a heat equation perturbed by a multiplicative noise of Itô type and under homogeneous Neumann boundary conditions. The idea is to adapt well-known methods in the de-terministic case for the approximation of parabolic problems to our stochastic PDE. In this paper, we try to highlight difficulties brought by the stochastic perturbation in the adaptation of these deterministic tools.

Mots clés: Stochastic heat equation; Itô integral; multiplicative noise; Itô formula; predictable process; Finite Volume Method

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Caroline Bauzet, Flore Nabet. Convergence of a finite-volume scheme for a heat equation with a multiplicative stochastic force. Finite Volumes for Complex Applications IX, Jun 2020, Bergen, Norway. ⟨hal-02442422v2⟩