Convergence of flux-splitting finite volume schemes for hyperbolic scalar conservation laws with a multiplicative stochastic perturbation

Bauzet, C.; Charrier, J.; Gallouët, T.

doi:10.1090/mcom/3084

Convergence of flux-splitting finite volume schemes for hyperbolic scalar conservation laws with a multiplicative stochastic perturbation
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by C. Bauzet, J. Charrier and T. Gallouët;

Math. Comp. 85 (2016), 2777-2813

DOI: https://doi.org/10.1090/mcom/3084

Published electronically: February 24, 2016

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Abstract:

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.

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