Convergence of a finite volume scheme for a stochastic conservation law involving a Q-Brownian motion

Tadahisa Funaki (1) , Yueyuan Gao (2) , Danielle Hilhorst (3)

1 UTokyo - The University of Tokyo
2 UP11 - Université Paris-Sud - Paris 11
3 LM-Orsay - Laboratoire de Mathématiques d'Orsay

We study a time explicit finite volume method with Godunov scheme for a rst order conservation law with a multiplicative source term involving a Q-Wiener process. We present some a priori estimates including a weak BV estimate. After performing a time interpolation, we prove two entropy inequalities for the discrete solution and show that it converges up to a subsequence to a stochastic measure-valued entropy solution of the conservation law in the sense of Young measures. Some numerical simulations are presented in the case of the stochastic Burgers equation.

Domaines: Equations aux dérivées partielles [math.AP]

Tadahisa Funaki, Yueyuan Gao, Danielle Hilhorst. Convergence of a finite volume scheme for a stochastic conservation law involving a Q-Brownian motion. 2017. ⟨hal-01404119v3⟩