In:
ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, Vol. 57, No. 2 ( 2023-03), p. 745-783
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.
Type of Medium:
Online Resource
ISSN:
2822-7840
,
2804-7214
DOI:
10.1051/m2an/2022087
Language:
English
Publisher:
EDP Sciences
Publication Date:
2023
detail.hit.zdb_id:
1485131-3
