TY - JOUR
T1 - Convergence of the Finite Volume Method for Stochastic Hyperbolic Scalar Conservation Laws: A Proof by Truncation on the Sample-Time Space
AU - Dotti , Sylvain
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 120
EP - 164
PY - 2024
DA - 2024/01
SN - 21
DO - http://doi.org/10.4208/ijnam2024-1005
UR - https://global-sci.org/intro/article_detail/ijnam/22331.html
KW - Finite volume method, stochastic balance law, kinetic formulation.
AB - <p style="text-align: justify;">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.</p>