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 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.
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Acknowledgements
The authors would like to thank the German Research Foundation, the Institut de Mécanique et d’Ingenierie of Marseille, the Programmes for Project-Related Personal Exchange Procope and Procope Plus and the Procope Mobility Program DEU-22-0004 LG1 for financial support.
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Bauzet, C., Nabet, F., Schmitz, K., Zimmermann, A. (2023). Finite Volume Approximations for Non-linear Parabolic Problems with Stochastic Forcing. In: Franck, E., Fuhrmann, J., Michel-Dansac, V., Navoret, L. (eds) Finite Volumes for Complex Applications X—Volume 1, Elliptic and Parabolic Problems. FVCA 2023. Springer Proceedings in Mathematics & Statistics, vol 432. Springer, Cham. https://doi.org/10.1007/978-3-031-40864-9_10
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DOI: https://doi.org/10.1007/978-3-031-40864-9_10
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