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 of with Dirichlet boundary conditions and a given initial data in . 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.
Accepté le :
DOI : 10.1051/m2an/2016020
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
@article{M2AN_2017__51_1_225_0,
author = {Bauzet, Caroline and Charrier, Julia and Gallou\"et, Thierry},
title = {Numerical approximation of stochastic conservation laws on bounded domains},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {225--278},
year = {2017},
publisher = {EDP Sciences},
volume = {51},
number = {1},
doi = {10.1051/m2an/2016020},
zbl = {1368.65007},
mrnumber = {3601008},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2016020/}
}
TY - JOUR AU - Bauzet, Caroline AU - Charrier, Julia AU - Gallouët, Thierry TI - Numerical approximation of stochastic conservation laws on bounded domains JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 225 EP - 278 VL - 51 IS - 1 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2016020/ DO - 10.1051/m2an/2016020 LA - en ID - M2AN_2017__51_1_225_0 ER -
%0 Journal Article %A Bauzet, Caroline %A Charrier, Julia %A Gallouët, Thierry %T Numerical approximation of stochastic conservation laws on bounded domains %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 225-278 %V 51 %N 1 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an/2016020/ %R 10.1051/m2an/2016020 %G en %F M2AN_2017__51_1_225_0
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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