Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

Request Permissions   Purchase Content 
 

 

Convergence of flux-splitting finite volume schemes for hyperbolic scalar conservation laws with a multiplicative stochastic perturbation


Authors: C. Bauzet, J. Charrier and T. Gallouët
Journal: Math. Comp. 85 (2016), 2777-2813
MSC (2010): Primary 35L60, 60H15, 65M08, 65M12
DOI: https://doi.org/10.1090/mcom/3084
Published electronically: February 24, 2016
MathSciNet review: 3522970
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Here, we study explicit flux-splitting finite volume discretizations of multi-dimensional nonlinear scalar conservation laws perturbed by a multiplicative noise with a given initial data in $ L^{2}(\mathbb{R}^d)$. Under a stability condition on the time step, we prove the convergence of the finite volume approximation towards the unique stochastic entropy solution of the equation.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 35L60, 60H15, 65M08, 65M12

Retrieve articles in all journals with MSC (2010): 35L60, 60H15, 65M08, 65M12


Additional Information

C. Bauzet
Affiliation: Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 13453 Marseille France
Email: caroline.bauzet@univ-amu.fr

J. Charrier
Affiliation: Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 13453 Marseille France
Email: julia.charrier@univ-amu.fr

T. Gallouët
Affiliation: Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 13453 Marseille France
Email: thierry.gallouet@univ-amu.fr

DOI: https://doi.org/10.1090/mcom/3084
Keywords: Stochastic PDE, first-order hyperbolic equation, It\^o integral, multiplicative noise, finite volume method, flux-splitting scheme, Engquist-Osher scheme, Lax-Friedrichs scheme, upwind scheme, Young measures, Kruzhkov smooth entropy
Received by editor(s): March 12, 2014
Received by editor(s) in revised form: December 13, 2014
Published electronically: February 24, 2016
Additional Notes: This work has been carried out in the framework of the Labex Archimède (ANR-11-LABX-0033) and of the A*MIDEX project (ANR-11-IDEX-0001-02), funded by the “Investissements d’Avenir” French Government programme managed by the French National Research Agency (ANR)
Article copyright: © Copyright 2016 American Mathematical Society