Convergence of the Finite Volume method for scalar conservation laws with multiplicative noise: an approach by kinetic formulation
Tóm tắt
Under a standard CFL condition, 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. In Dotti and Vovelle (Arch Ration Mech Anal 230(2):539–591, 2018), a framework for the analysis of the convergence of approximations to stochastic scalar first-order conservation laws has been developed, on the basis of a kinetic formulation. Here, we give a kinetic formulation of the numerical method, analyse its properties, and explain how to cast the problem of convergence of the numerical scheme into the framework of Dotti and Vovelle
(2018). This uses standard estimates (like the so-called “weak BV estimate”, for which we give a proof using specifically the kinetic formulation) and an adequate interpolation procedure.
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