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While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC finite element approach based on deterministic adaptive mesh refinement for the arising “pathwise” problems and outline a convergence theory in terms of desired accuracy and required computational cost. Our theoretical and heuristic reasoning together with the efficiency of our new approach are confirmed by numerical experiments.

Adaptive Multilevel Monte Carlo Methods for Stochastic Variational Inequalities