%0 Journal Article
%T Numerical approximation of stochastic conservation laws on bounded domains
%+ Laboratoire de Mécanique et d'Acoustique [Marseille] (LMA )
%+ Institut de Mathématiques de Marseille (I2M)
%A Bauzet, Caroline
%A Charrier, Julia
%A Gallouët, Thierry
%< avec comité de lecture
%@ 0764-583X
%J ESAIM: Mathematical Modelling and Numerical Analysis
%I EDP Sciences
%8 2016-03-11
%D 2016
%R 10.1051/m2an/2016020
%K Stochastic PDE
%K first-order hyperbolic equation
%K multiplicative noise
%K finite volume method
%K monotone scheme
%K Dirichlet boundary conditions.
%Z 35L60 ● 60H15 ● 35L60
%Z Mathematics [math]/Analysis of PDEs [math.AP]Journal articles
%X 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.
%G English
%2 https://hal.science/hal-01197259/document
%2 https://hal.science/hal-01197259/file/Boundaryconditions.pdf
%L hal-01197259
%U https://hal.science/hal-01197259
%~ CNRS
%~ UNIV-AMU
%~ LMA_UPR7051
%~ EC-MARSEILLE
%~ I2M
%~ I2M-2014-
%~ TDS-MACS
%~ PEIRESC