Finite Volume Approximations for Non-linear Parabolic Problems with Stochastic Forcing

Caroline Bauzet; Flore Nabet; Kerstin Schmitz; Aleksandra Zimmermann

doi:10.1007/978-3-031-40864-9_10

Finite Volume Approximations for Non-linear Parabolic Problems with Stochastic Forcing

Caroline Bauzet
, Flore Nabet
, Kerstin Schmitz
, Aleksandra Zimmermann

Aix Marseille Université
University of Duisburg-Essen
TU Clausthal

Résultats de recherche: Le chapitre dans un livre, un rapport, une anthologie ou une collection › Contribution à une conférence › Revue par des pairs

Résumé

We propose a two-point flux approximation finite-volume scheme for a stochastic non-linear parabolic equation with a multiplicative noise. The time discretization is implicit except for the stochastic noise term in order to be compatible with stochastic integration in the sense of Itô. We show existence and uniqueness of solutions to the scheme and the appropriate measurability for stochastic integration follows from the uniqueness of approximate solutions.

langue originale	Anglais
titre	Finite Volumes for Complex Applications 10—Volume 1, Elliptic and Parabolic Problems - FVCA10, 2023, Invited Contributions
rédacteurs en chef	Emmanuel Franck, Victor Michel-Dansac, Laurent Navoret, Jürgen Fuhrmann
Editeur	Springer
Pages	157-166
Nombre de pages	10
ISBN (imprimé)	9783031408632
Les DOIs	https://doi.org/10.1007/978-3-031-40864-9_10
état	Publié - 1 janv. 2023
Evénement	10th International Symposium on Finite Volumes for Complex Applications, FVCA10 2023 - Strasbourg, France Durée: 30 oct. 2023 → 3 nov. 2023

Série de publications

Nom	Springer Proceedings in Mathematics and Statistics
Volume	432
ISSN (imprimé)	2194-1009
ISSN (Electronique)	2194-1017

Une conférence

Une conférence	10th International Symposium on Finite Volumes for Complex Applications, FVCA10 2023
Pays/Territoire	France
La ville	Strasbourg
période	30/10/23 → 3/11/23

Accès au document

10.1007/978-3-031-40864-9_10

Contient cette citation

Bauzet, C., Nabet, F., Schmitz, K., & Zimmermann, A. (2023). Finite Volume Approximations for Non-linear Parabolic Problems with Stochastic Forcing. Dans E. Franck, V. Michel-Dansac, L. Navoret, & J. Fuhrmann (eds.), Finite Volumes for Complex Applications 10—Volume 1, Elliptic and Parabolic Problems - FVCA10, 2023, Invited Contributions (p. 157-166). (Springer Proceedings in Mathematics and Statistics; Vol 432). Springer. https://doi.org/10.1007/978-3-031-40864-9_10

Bauzet, Caroline ; Nabet, Flore ; Schmitz, Kerstin et al. / Finite Volume Approximations for Non-linear Parabolic Problems with Stochastic Forcing. Finite Volumes for Complex Applications 10—Volume 1, Elliptic and Parabolic Problems - FVCA10, 2023, Invited Contributions. Editeur / Emmanuel Franck ; Victor Michel-Dansac ; Laurent Navoret ; Jürgen Fuhrmann. Springer, 2023. p. 157-166 (Springer Proceedings in Mathematics and Statistics).

@inproceedings{4807421d28c2492e927856947f4a4003,

title = "Finite Volume Approximations for Non-linear Parabolic Problems with Stochastic Forcing",

abstract = "We propose a two-point flux approximation finite-volume scheme for a stochastic non-linear parabolic equation with a multiplicative noise. The time discretization is implicit except for the stochastic noise term in order to be compatible with stochastic integration in the sense of It{\^o}. We show existence and uniqueness of solutions to the scheme and the appropriate measurability for stochastic integration follows from the uniqueness of approximate solutions.",

keywords = "Diffusion-convection equation, Finite-volume method, Multiplicative Lipschitz noise, Stochastic non-linear parabolic equation, Upwind scheme, Variational approach",

author = "Caroline Bauzet and Flore Nabet and Kerstin Schmitz and Aleksandra Zimmermann",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.; 10th International Symposium on Finite Volumes for Complex Applications, FVCA10 2023 ; Conference date: 30-10-2023 Through 03-11-2023",

year = "2023",

month = jan,

day = "1",

doi = "10.1007/978-3-031-40864-9\_10",

language = "English",

isbn = "9783031408632",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer",

pages = "157--166",

editor = "Emmanuel Franck and Victor Michel-Dansac and Laurent Navoret and J{\"u}rgen Fuhrmann",

booktitle = "Finite Volumes for Complex Applications 10—Volume 1, Elliptic and Parabolic Problems - FVCA10, 2023, Invited Contributions",

}

Bauzet, C, Nabet, F, Schmitz, K & Zimmermann, A 2023, Finite Volume Approximations for Non-linear Parabolic Problems with Stochastic Forcing. Dans E Franck, V Michel-Dansac, L Navoret & J Fuhrmann (eds), Finite Volumes for Complex Applications 10—Volume 1, Elliptic and Parabolic Problems - FVCA10, 2023, Invited Contributions. Springer Proceedings in Mathematics and Statistics, VOL. 432, Springer, p. 157-166, 10th International Symposium on Finite Volumes for Complex Applications, FVCA10 2023, Strasbourg, France, 30/10/23. https://doi.org/10.1007/978-3-031-40864-9_10

Finite Volume Approximations for Non-linear Parabolic Problems with Stochastic Forcing. / Bauzet, Caroline; Nabet, Flore; Schmitz, Kerstin et al.
Finite Volumes for Complex Applications 10—Volume 1, Elliptic and Parabolic Problems - FVCA10, 2023, Invited Contributions. Ed. / Emmanuel Franck; Victor Michel-Dansac; Laurent Navoret; Jürgen Fuhrmann. Springer, 2023. p. 157-166 (Springer Proceedings in Mathematics and Statistics; Vol 432).

Résultats de recherche: Le chapitre dans un livre, un rapport, une anthologie ou une collection › Contribution à une conférence › Revue par des pairs

TY - GEN

T1 - Finite Volume Approximations for Non-linear Parabolic Problems with Stochastic Forcing

AU - Bauzet, Caroline

AU - Nabet, Flore

AU - Schmitz, Kerstin

AU - Zimmermann, Aleksandra

PY - 2023/1/1

Y1 - 2023/1/1

N2 - We propose a two-point flux approximation finite-volume scheme for a stochastic non-linear parabolic equation with a multiplicative noise. The time discretization is implicit except for the stochastic noise term in order to be compatible with stochastic integration in the sense of Itô. We show existence and uniqueness of solutions to the scheme and the appropriate measurability for stochastic integration follows from the uniqueness of approximate solutions.

AB - We propose a two-point flux approximation finite-volume scheme for a stochastic non-linear parabolic equation with a multiplicative noise. The time discretization is implicit except for the stochastic noise term in order to be compatible with stochastic integration in the sense of Itô. We show existence and uniqueness of solutions to the scheme and the appropriate measurability for stochastic integration follows from the uniqueness of approximate solutions.

KW - Diffusion-convection equation

KW - Finite-volume method

KW - Multiplicative Lipschitz noise

KW - Stochastic non-linear parabolic equation

KW - Upwind scheme

KW - Variational approach

U2 - 10.1007/978-3-031-40864-9_10

DO - 10.1007/978-3-031-40864-9_10

M3 - Conference contribution

AN - SCOPUS:85174489803

SN - 9783031408632

T3 - Springer Proceedings in Mathematics and Statistics

SP - 157

EP - 166

BT - Finite Volumes for Complex Applications 10—Volume 1, Elliptic and Parabolic Problems - FVCA10, 2023, Invited Contributions

A2 - Franck, Emmanuel

A2 - Michel-Dansac, Victor

A2 - Navoret, Laurent

A2 - Fuhrmann, Jürgen

PB - Springer

T2 - 10th International Symposium on Finite Volumes for Complex Applications, FVCA10 2023

Y2 - 30 October 2023 through 3 November 2023

ER -