Article Dans Une Revue ESAIM: Mathematical Modelling and Numerical Analysis Année : 2016

Numerical approximation of stochastic conservation laws on bounded domains

Résumé

This paper is devoted to the study of finite volume methods for the discretization of scalar conservation laws with a multiplicative stochastic force defined on a bounded domain D of R d with Dirichlet boundary conditions and a given initial data in L ∞ (D). We introduce a notion of stochastic entropy process solution which generalizes the concept of weak entropy solution introduced by F.Otto for such kind of hyperbolic bounded value problems in the deterministic case. Using a uniqueness result on this solution, we prove that the numerical solution converges to the unique stochastic entropy weak solution of the continuous problem under a stability condition on the time and space steps.

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hal-01197259 , version 1 (11-09-2015)

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Caroline Bauzet, Julia Charrier, Thierry Gallouët. Numerical approximation of stochastic conservation laws on bounded domains. ESAIM: Mathematical Modelling and Numerical Analysis, 2016, ⟨10.1051/m2an/2016020⟩. ⟨hal-01197259⟩
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