Convergence of the Finite Volume Method for scalar conservation laws with multiplicative noise: an approach by kinetic formulation

TL;DR

This paper proves the convergence of an explicit finite volume method for scalar conservation laws affected by multiplicative noise, using a kinetic formulation approach.

Contribution

It introduces a novel convergence proof for finite volume schemes applied to stochastic conservation laws with multiplicative noise via kinetic methods.

Findings

Finite volume method converges for stochastic conservation laws.

Kinetic formulation effectively handles multiplicative noise.

Provides theoretical foundation for numerical schemes under stochastic influences.

Abstract

We prove the convergence of the explicit-in-time Finite Volume method with monotone fluxes for the approximation of scalar first-order conservation laws with multiplicative, compactly supported noise.