| Issue |
ESAIM: M2AN
Volume 57, Number 2, March-April 2023
|
|
|---|---|---|
| Page(s) | 745 - 783 | |
| DOI | https://doi.org/10.1051/m2an/2022087 | |
| Published online | 27 March 2023 | |
Convergence of a finite-volume scheme for a heat equation with a multiplicative Lipschitz noise
1
Aix Marseille Univ, CNRS, Centrale Marseille, LMA UMR 7031, Marseille, France
2
CMAP, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau, France
3
Universität Duisburg-Essen, Fakultät für Mathematik, Essen, Germany
* Corresponding author: kerstin.schmitz@uni-due.de
Received:
9
May
2022
Accepted:
20
October
2022
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.
Mathematics Subject Classification: 60H15 / 35K05 / 65M08
Key words: Stochastic heat equation / multiplicative Lipschitz noise / finite-volume method / stochastic compactness method / variational approach / convergence analysis
© The authors. Published by EDP Sciences, SMAI 2023
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