TY - JOUR
T1 - Multilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations
JF - Numerische Mathematik, (2015), 36 p. Article in Press
Y1 - 2015
A1 - Gianluigi Rozza
A1 - Peng Chen
A1 - Alfio Quarteroni
AB - In 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.
PB - Springer
UR - http://urania.sissa.it/xmlui/handle/1963/34491
U1 - 34680
U2 - Mathematics
U4 - 1
U5 - MAT/08
ER -