Geodesic
Numerical approximation of stochastic conservation laws on bounded domains
Bauzet, Caroline1 idref ; Charrier, Julia2 idref ; Gallouët, Thierry2 idref
1LMA, Aix-Marseille Univ, CNRS, UPR 7051, Centrale Marseille, 13402 Marseille cedex 20, France.
2I2M, Aix-Marseille Univ, CNRS, UMR 7373, Centrale Marseille, 13453 Marseille, France.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 1, pp. 225-278

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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.

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2016020
Classification : 35L60, 60H15, 35L60
Keywords: Stochastic PDE, first-order hyperbolic equation, multiplicative noise, finite volume method, monotone scheme, Dirichlet boundary conditions

Bauzet, Caroline  1   ; Charrier, Julia  2   ; Gallouët, Thierry  2

1 LMA, Aix-Marseille Univ, CNRS, UPR 7051, Centrale Marseille, 13402 Marseille cedex 20, France.
2 I2M, Aix-Marseille Univ, CNRS, UMR 7373, Centrale Marseille, 13453 Marseille, France. 
Bauzet, Caroline; Charrier, Julia; Gallouët, Thierry. Numerical approximation of stochastic conservation laws on bounded domains. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 1, pp. 225-278. doi: 10.1051/m2an/2016020
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     title = {Numerical approximation of stochastic conservation laws on bounded domains},
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     pages = {225--278},
     year = {2017},
     publisher = {EDP-Sciences},
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