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Convergence of flux-splitting finite volume schemes for hyperbolic scalar conservation laws with a multiplicative stochastic perturbation. (English) Zbl 1351.65003
Summary: Here, we study explicit flux-splitting finite volume discretizations of multi-dimensional nonlinear scalar conservation laws perturbed by a multiplicative noise with a given initial data in $$L^{2}(\mathbb{R}^d)$$. Under a stability condition on the time step, we prove the convergence of the finite volume approximation towards the unique stochastic entropy solution of the equation.

##### MSC:
 65C30 Numerical solutions to stochastic differential and integral equations 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs 35L65 Hyperbolic conservation laws 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 35R60 PDEs with randomness, stochastic partial differential equations 60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
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