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Archive for Rational Mechanics and Analysis

, Volume 230, Issue 2, pp 539–591 | Cite as

Convergence of Approximations to Stochastic Scalar Conservation Laws

  • Sylvain Dotti
  • Julien Vovelle
Article
  • 71 Downloads

Abstract

We develop a general framework for the analysis of approximations to stochastic scalar conservation laws. Our aim is to prove, under minimal consistency properties and bounds, that such approximations are converging to the solution to a stochastic scalar conservation law. The weak probabilistic convergence mode is convergence in law, the most natural in this context. We use also a kinetic formulation and martingale methods. Our result is applied to the convergence of the finite volume method in the companion paper (Dotti and Vovelle in Convergence of the finite volume method for scalar conservation laws with multiplicative noise: an approach by kinetic formulation, 2016).

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373MarseilleFrance
  2. 2.Univ Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille JordanVilleurbanne CedexFrance

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