Convergence of the Finite Volume Method for Stochastic Hyperbolic Scalar Conservation Laws: A Proof by Truncation on the Sample-Time Space
Year: 2024
Author: Sylvain Dotti
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 1 : pp. 120–164
Abstract
We prove the almost sure convergence of the explicit-in-time Finite Volume Method with monotone fluxes towards the unique solution of the scalar hyperbolic balance law with locally Lipschitz continuous flux and additive noise driven by a cylindrical Wiener process. We use the standard CFL condition and a martingale exponential inequality on sets whose probabilities are converging towards one. Then, with the help of stopping times on those sets, we apply theorems of convergence for approximate kinetic solutions of balance laws with stochastic forcing.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2024-1005
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 1 : pp. 120–164
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 45
Keywords: Finite volume method stochastic balance law kinetic formulation.