Convergence of a TPFA scheme for a diffusion-convection equation with a multiplicative stochastic noise
| Autor: | Bauzet, Caroline, Schmitz, Kerstin, Zimmermann, Aleksandra |
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| Přispěvatelé: | Laboratoire de Mécanique et d'Acoustique [Marseille] (LMA ), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Universität Duisburg-Essen = University of Duisburg-Essen [Essen], TU Clausthal, Institut für Mathematik, Clausthal-Zellerfeld, Procope programs: Project-Related Personal Exchange France-Germany (49368YE), Procope Mobility Program (DEU-22-0004 LG1) and Procope Plus Project, European Project |
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: |
Variational approach
Mathematics Subject Classification (2020): 60H15 • 35K05 • 65M08 Numerical Analysis (math.NA) Finite-volume method 60H15 35K05 65M08 Diffusion-convection equation Convergence analysis Mathematics Mathematics - Analysis of PDEs Upwind scheme FOS: Mathematics Mathematics - Numerical Analysis Stochastic non-linear parabolic equation Multiplicative Lipschitz noise [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] Analysis of PDEs (math.AP) |
| Popis: | 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 $\mathbb{R}^2$ 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 $L^2(\Omega; L^2(0,T;L^2(\Lambda)))$. Comment: arXiv admin note: text overlap with arXiv:2203.09851 |
| Databáze: | OpenAIRE |
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