Convergence of a flux-splitting finite volume scheme for conservation laws driven by L\'{e}vy noise

TL;DR

This paper proves the convergence of a flux-splitting finite volume scheme for multidimensional stochastic conservation laws driven by Lévy noise, ensuring accurate numerical approximation of the entropy solution.

Contribution

It introduces and analyzes a flux-splitting finite volume method specifically designed for stochastic conservation laws with Lévy noise, establishing convergence to the entropy solution.

Findings

Proved convergence of the scheme to the entropy solution.

Validated the method for multidimensional stochastic conservation laws.

Provided theoretical foundation for numerical approximation with Lévy noise.

Abstract

We explore numerical approximation of multidimensional stochastic balance laws driven by multiplicative L\'{e}vy noise via flux- splitting finite volume method. The convergence of the approximations is proved towards the unique entropy solution of the underlying problem.