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Journal Articles ESAIM: Mathematical Modelling and Numerical Analysis Year : 2022

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

Abstract

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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Dates and versions

hal-03663571 , version 1 (10-05-2022)
hal-03663571 , version 2 (27-10-2022)

Identifiers

Cite

Caroline Bauzet, Flore Nabet, Kerstin Schmitz, Aleksandra Zimmermann. Convergence of a finite-volume scheme for a heat equation with a multiplicative Lipschitz noise. ESAIM: Mathematical Modelling and Numerical Analysis, In press, 57 (2), pp.745-783. ⟨10.1051/m2an/2022087⟩. ⟨hal-03663571v2⟩
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