Multilevel Monte Carlo finite volume methods for random conservation laws with discontinuous flux

We consider conservation laws with discontinuous flux where the initial datum, function, and spatial dependency coefficient are subject to randomness. establish a notion of random adapted entropy solutions these equations prove well-posedness provided that is piecewise constant finitely many discontinuities. In particular, setting under consideration allows change across points in space whose positions uncertain. propose single- multilevel Monte Carlo method based on finite volume approximation for each sample. Our analysis includes convergence rate estimates resulting methods as well error versus work rates showing variant outperforms single-level terms efficiency. present numerical experiments motivated by two-phase reservoir simulations reservoirs varying geological properties.