Volume 51, Number 1, January-February 2017
|Page(s)||225 - 278|
|Published online||02 December 2016|
Numerical approximation of stochastic conservation laws on bounded domains
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.
Received: 11 September 2015
Accepted: 11 March 2016
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 Rd 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.
Mathematics Subject Classification: 35L60 / 60H15 / 35L60
Key words: Stochastic PDE / first-order hyperbolic equation / multiplicative noise / finite volume method / monotone scheme / Dirichlet boundary conditions
© EDP Sciences, SMAI 2016
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.