A Priori Error Estimate of Stochastic Galerkin Method for Optimal Control Problem Governed by Random Parabolic PDE with Constrained Control

Gong, Benxue and Sun, Tongjun and Shen, Wanfang and Liu, Wenbin (2016) A Priori Error Estimate of Stochastic Galerkin Method for Optimal Control Problem Governed by Random Parabolic PDE with Constrained Control. International Journal of Computational Methods, 13 (5). ISSN 0219-8762. E-ISSN 1793-6969. (doi:https://doi.org/10.1142/S0219876216500286) (Full text available)

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http://dx.doi.org/10.1142/S0219876216500286

Abstract

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.

Item Type: Article
Uncontrolled keywords: Priori error estimates; stochastic Galerkin method; optimal control problem; random parabolic PDE; obstacle control constraint.
Divisions: Faculties > Social Sciences > Kent Business School
Depositing User: Steve Wenbin Liu
Date Deposited: 06 Mar 2017 12:41 UTC
Last Modified: 06 Mar 2017 12:52 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/60737 (The current URI for this page, for reference purposes)
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