标题：A Priori Error Estimate of Stochastic Galerkin Method for Optimal Control Problem Governed by Random Parabolic PDE with Constrained Control
作者：Gong, Benxue; Sun, Tongjun; Shen, Wanfang; Liu, Wenbin
作者机构：[Gong, Benxue] Shandong Univ Technol, Sch Sci, Zibo 255049, Peoples R China.; [Sun, Tongjun] Shandong Univ, Sch Math, Jinan 250100, Peoples R China. 更多
通讯作者地址：[Gong, BX]Shandong Univ Technol, Sch Sci, Zibo 255049, Peoples R China.
来源：INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS
关键词：Priori error estimates; stochastic Galerkin method; optimal control; problem; random parabolic PDE; obstacle control constraint
摘要：A stochastic Galerkin approximation scheme is proposed for an optimal control problem governed by a parabolic PDE with random perturbation in its coefficients. The objective functional is to minimize the expectation of a cost functional, and the deterministic control is of the obstacle constrained type. We obtain the necessary and sufficient optimality conditions and establish a scheme to approximate the optimality system through the discretization with respect to both the spatial space and the probability space by Galerkin method and with respect to time by the backward Euler scheme. A priori error estimates are derived for the state, the co-state and the control variables. Numerical examples are presented to illustrate our theoretical results.