  The Richards' equation is a model for flow of water in unsaturated soils. The
coefficients of this (nonlinear) partial differential equation describe the
permeability of the medium. Insufficient or uncertain measurements are commonly
modeled by random coefficients. For flows in heterogeneous\textbackslash
fractured\textbackslash porous media, the coefficients are modeled as
discontinuous random fields, where the interfaces along the stochastic
discontinuities represent transitions in the media. More precisely, the random
coefficient is given by the sum of a (continuous) Gaussian random field and a
(discontinuous) jump part. In this work moments of the solution to the random
partial differential equation are calculated using a path-wise numerical
approximation combined with multilevel Monte Carlo sampling. The
discontinuities dictate the spatial discretization, which leads to a stochastic
grid. Hence, the refinement parameter and problem-dependent constants in the
error analysis are random variables and we derive (optimal) a-priori
convergence rates in a mean-square sense.
