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General elliptic equations with spatially discontinuous diffusioncoefficients may be used as a simplified model for subsurface flow inheterogeneous or fractured porous media. In such a model, data sparsity andmeasurement errors are often taken into account by a randomization of thediffusion coefficient of the elliptic equation which reveals the necessity ofthe construction of flexible, spatially discontinuous random fields.Subordinated Gaussian random fields are random functions on higher dimensionalparameter domains with discontinuous sample paths and great distributionalflexibility. In the present work, we consider a random elliptic partialdifferential equation (PDE) where the discontinuous subordinated Gaussianrandom fields occur in the diffusion coefficient. Problem specific multilevelMonte Carlo (MLMC) Finite Element methods are constructed to approximate themean of the solution to the random elliptic PDE. We prove a-priori convergenceof a standard MLMC estimator and a modified MLMC - Control Variate estimatorand validate our results in various numerical examples.

Multilevel Monte Carlo estimators for elliptic PDEs with L\'evy-type diffusion coefficient