Convergence of a finite-volume scheme for a heat equation with a multiplicative Lipschitz noise - Ecole Centrale de Marseille Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2022

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

Résumé

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. Since the nonlinearity in the stochastic integral is not compatible with the weak convergence obtained by the a priori estimates, we adapt the method based on the theorem of Prokhorov and on Skorokhod's representation theorem in order to show stochastically strong convergence of the scheme towards the unique variational solution of our parabolic problem.
Fichier principal
Vignette du fichier
Bauzet_Nabet_Schmitz_Zimmermann_Hal.pdf (613.57 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

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

Identifiants

  • HAL Id : hal-03663571 , version 1

Citer

Caroline Bauzet, Flore Nabet, Kerstin Schmitz, Aleksandra Zimmermann. Convergence of a finite-volume scheme for a heat equation with a multiplicative Lipschitz noise. 2022. ⟨hal-03663571v1⟩
183 Consultations
105 Téléchargements

Partager

Gmail Facebook X LinkedIn More