| Autor: |
Bauzet, Caroline, Nabet, Flore, Schmitz, Kerstin, Zimmermann, Aleksandra |
| Rok vydání: |
2022 |
| Předmět: |
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| Zdroj: |
ESAIM Math. Model. Numer. Anal. 57 (2023), no.2, 745-783 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1051/m2an/2022087 |
| Popis: |
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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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