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We present an adaptive multilevel Monte Carlo algorithm for solving thestochastic drift-diffusion-Poisson system with non-zero recombination rate. Thea-posteriori error is estimated to enable goal-oriented adaptive meshrefinement for the spatial dimensions, while the a-priori error is estimated toguarantee \red{linear} convergence of the $H^1$ error. In the adaptive meshrefinement, efficient estimation of the error indicator gives rise to bettererror control. For the stochastic dimensions, we use the multilevel Monte Carlomethod to solve this system of stochastic partial differential equations.Finally, the advantage of the technique developed here compared to uniform meshrefinement is discussed using a realistic numerical example.

An adaptive multilevel Monte Carlo algorithm for the stochastic drift-diffusion-Poisson system