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.

中文翻译：

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具有乘性噪声的标量守恒律的有限体积方法的收敛：一种动力学公式方法

在标准的CFL条件下，我们证明了具有单调通量的及时显式有限体积方法的收敛性，用于逼近标量一阶守恒律和可压缩的紧凑噪声。在Dotti和Vovelle（Arch Ration Mech Anal 230（2）：539–591，2018）中，基于动力学公式，已经开发出了一个框架，用于分析近似于随机标量一阶守恒律的收敛性。 。在这里，我们给出了数值方法的动力学公式，分析了它的性质，并解释了如何将数值方案的收敛问题投射到Dotti和Vovelle（2018）的框架中。这使用标准估算值（例如所谓的“弱BV估算”，