PDE seminar by Håkon Hoel (UiO)

Stochastic conservation laws (SCL) with quasilinear multiplicative rough path dependence arise in modeling of mean field games. An impressive collection of theoretical results has been developed for SCL in recent years by Gess, Lions, Perthame, and Souganidis. In this talk we present numerical methods for pathwise solutions of scalar SCL with, for instance, Gaussian randomness in rough fluxes. We provide convergence rates for the numerical methods and show how rough path oscillations may lead to cancellations in the flow map solution operator, which again leads to more efficient numerical methods.