  General elliptic equations with spatially discontinuous diffusion
coefficients may be used as a simplified model for subsurface flow in
heterogeneous or fractured porous media. In such a model, data sparsity and
measurement errors are often taken into account by a randomization of the
diffusion coefficient of the elliptic equation which reveals the necessity of
the construction of flexible, spatially discontinuous random fields.
Subordinated Gaussian random fields are random functions on higher dimensional
parameter domains with discontinuous sample paths and great distributional
flexibility. In the present work, we consider a random elliptic partial
differential equation (PDE) where the discontinuous subordinated Gaussian
random fields occur in the diffusion coefficient. Problem specific multilevel
Monte Carlo (MLMC) Finite Element methods are constructed to approximate the
mean of the solution to the random elliptic PDE. We prove a-priori convergence
of a standard MLMC estimator and a modified MLMC - Control Variate estimator
and validate our results in various numerical examples.
