01516nas a2200133   4500008004100000245012100041210006900162260001300231520102900244100002101273700001501294700002201309856005101331       2015                        en  d00aMultilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations0 aMultilevel and weighted reduced basis method for stochastic opti  bSpringer3 aIn this paper we develop and analyze a multilevel weighted reduced basis method for solving stochastic optimal control problems constrained by Stokes equations. We prove the analytic regularity of the optimal solution in the probability space under certain assumptions on the random input data. The finite element method and the stochastic collocation method are employed for the numerical approximation of the problem in the deterministic space and the probability space, respectively, resulting in many large-scale optimality systems to solve. In order to reduce the unaffordable computational effort, we propose a reduced basis method using a multilevel greedy algorithm in combination with isotropic and anisotropic sparse-grid techniques. A weighted a posteriori error bound highlights the contribution stemming from each method. Numerical tests on stochastic dimensions ranging from 10 to 100 demonstrate that our method is very efficient, especially for solving high-dimensional and large-scale optimization problems.1 aRozza, Gianluigi1 aChen, Peng1 aQuarteroni, Alfio  uhttp://urania.sissa.it/xmlui/handle/1963/34491