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arXiv · 2203.09851

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

Caroline Bauzet·Flore Nabet·Kerstin Schmitz·Aleksandra Zimmermann
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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 It\^o. 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 Gy\"{o}ngy-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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Caroline Bauzet, Flore Nabet, Kerstin Schmitz, Aleksandra Zimmermann. 2022-03-18. Convergence of a finite-volume scheme for a heat equation with a multiplicative Lipschitz noise. https://doi.org/10.1051/m2an%2F2022087

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