Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Finite-Volume approximation of the invariant measure of a viscous stochastic scalar conservation law

Abstract : We aim to give a numerical approximation of the invariant measure of a viscous scalar conservation law, one-dimensional and periodic in the space variable, and stochastically forced with a white-in-time but spatially correlated noise. The flux function is assumed to be locally Lipschitz and to have at most polynomial growth. The numerical scheme we employ discretises the SPDE according to a finite volume method in space, and a split-step backward Euler method in time. As a first result, we prove the well-posedness as well as the existence and uniqueness of an invariant measure for both the spatial semi-discretisation and the fully discrete scheme. Our main result is then the convergence of the invariant measures of the discrete approximations, as the space and time steps go to zero, towards the invariant measure of the SPDE, with respect to the second-order Wasserstein distance. A few numerical experiments are performed to illustrate these results.
Complete list of metadatas

Cited literature [32 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02291253
Contributor : Sofiane Martel <>
Submitted on : Thursday, September 19, 2019 - 11:36:01 AM
Last modification on : Thursday, March 5, 2020 - 3:28:24 PM
Document(s) archivé(s) le : Saturday, February 8, 2020 - 11:19:12 PM

Files

InvariantMeasureApproximation....
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02291253, version 1
  • ARXIV : 1909.08899

Collections

Citation

Sébastien Boyaval, Sofiane Martel, Julien Reygner. Finite-Volume approximation of the invariant measure of a viscous stochastic scalar conservation law. 2019. ⟨hal-02291253⟩

Share

Metrics

Record views

147

Files downloads

45