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October, 2017 A Nonconforming Finite Element Method for Constrained Optimal Control Problems Governed by Parabolic Equations
Hong-Bo Guan, Dong-Yang Shi
Taiwanese J. Math. 21(5): 1193-1211 (October, 2017). DOI: 10.11650/tjm/7929

Abstract

In this paper, a nonconforming finite element method (NFEM) is proposed for the constrained optimal control problems (OCPs) governed by parabolic equations. The time discretization is based on the finite difference methods. The state and co-state variables are approximated by the nonconforming $EQ_1^{\operatorname{rot}}$ elements, and the control variable is approximated by the piecewise constant element, respectively. Some superclose properties are obtained for the above three variables. Moreover, for the state and co-state, the convergence and superconvergence results are achieved in $L^2$-norm and the broken energy norm, respectively.

Citation

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Hong-Bo Guan. Dong-Yang Shi. "A Nonconforming Finite Element Method for Constrained Optimal Control Problems Governed by Parabolic Equations." Taiwanese J. Math. 21 (5) 1193 - 1211, October, 2017. https://doi.org/10.11650/tjm/7929

Information

Received: 2 May 2016; Revised: 24 September 2016; Accepted: 25 December 2016; Published: October, 2017
First available in Project Euclid: 1 August 2017

zbMATH: 06871365
MathSciNet: MR3707890
Digital Object Identifier: 10.11650/tjm/7929

Subjects:
Primary: 65N30
Secondary: 65N15

Rights: Copyright © 2017 The Mathematical Society of the Republic of China

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Vol.21 • No. 5 • October, 2017
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