Geodesic
Numerical approximation of stochastic conservation laws on bounded domains
Bauzet, Caroline1  ; Charrier, Julia2  ; Gallouët, Thierry2 
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.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 1, pp. 225-278

Voir la notice de l'article provenant de la source Numdam

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. 
@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},
     publisher = {EDP-Sciences},
     volume = {51},
     number = {1},
     year = {2017},
     doi = {10.1051/m2an/2016020},
     zbl = {1368.65007},
     mrnumber = {3601008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/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  - http://geodesic.mathdoc.fr/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 http://geodesic.mathdoc.fr/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

Cité par Sources :