Treffer: On a finite-volume approximation of a diffusion-convection equation with a multiplicative stochastic force

Title:
On a finite-volume approximation of a diffusion-convection equation with a multiplicative stochastic force
Authors:
Bauzet, Caroline, Schmitz, Kerstin, Zimmermann, Aleksandra
Contributors:
Laboratoire de Mécanique et d'Acoustique [Marseille] (LMA), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Aix-Marseille Université - Faculté des Sciences (AMU SCI), Aix Marseille Université (AMU), Universität Duisburg-Essen = University of Duisburg-Essen [Essen], Technische Universität Clausthal = Clausthal University of Technology (TU Clausthal), Procope programs: Project-Related Personal Exchange France-Germany (49368YE), Procope Mobility Program (DEU-22-0004 LG1) and Procope Plus Project, European Project
Source:
Stochastics and Partial Differential Equations: Analysis and Computations. 13(4):2039-2084
Publisher Information:
CCSD; Springer US, 2025.
Publication Year:
2025
Collection:
collection:CNRS
collection:UNIV-AMU
collection:LMA_UPR7051
collection:EC-MARSEILLE
collection:TDS-MACS
collection:PEIRESC
collection:IMI-AMU
Subject Terms:
Variational approach, Convergence analysis Mathematics, Diffusion-convection equation, Upwind scheme, Finite-volume method, Multiplicative Lipschitz noise, Stochastic non-linear parabolic equation, Mathematics Subject Classification (2020): 60H15 • 35K05 • 65M08, [MATH.MATH-NA]Mathematics [math], Numerical Analysis [math.NA]
Original Identifier:
HAL: hal-04077628
Document Type:
Zeitschrift article<br />Journal articles
Language:
English
ISSN:
2194-0401
2194-041X
Relation:
info:eu-repo/semantics/altIdentifier/doi/10.1007/s40072-025-00379-8
DOI:
10.1007/s40072-025-00379-8
Access URL:
https://hal.science/hal-04077628
https://hal.science/hal-04077628v2/document
https://hal.science/hal-04077628v2/file/BSZ_revision_2025.pdf
Rights:
info:eu-repo/semantics/OpenAccess
Accession Number:
edshal.hal.04077628v2
Database:
HAL

Weitere Informationen

The aim of this paper is to address the convergence analysis of a finite-volume scheme for the approximation of a stochastic non-linear parabolic problem set in a bounded domain of R 2 and under homogeneous Neumann boundary conditions. The considered discretization is semi-implicit in time and TPFA in space. By adapting well-known methods for the time-discretization of stochastic PDEs, one shows that the associated finite-volume approximation converges towards the unique variational solution of the continuous problem strongly in L 2 (Ω; L 2 (0, T ; L 2 (Λ))).