Taiwanese Journal of Mathematics

A Nonconforming Finite Element Method for Constrained Optimal Control Problems Governed by Parabolic Equations

Hong-Bo Guan and Dong-Yang Shi

Full-text: Open access

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.

Article information

Source
Taiwanese J. Math., Volume 21, Number 5 (2017), 1193-1211.

Dates
Received: 2 May 2016
Revised: 24 September 2016
Accepted: 25 December 2016
First available in Project Euclid: 1 August 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1501599189

Digital Object Identifier
doi:10.11650/tjm/7929

Mathematical Reviews number (MathSciNet)
MR3707890

Zentralblatt MATH identifier
06871365

Subjects
Primary: 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Secondary: 65N15: Error bounds

Keywords
nonconforming finite element method parabolic optimal control problems supercloseness convergence and superconvergence

Citation

Guan, Hong-Bo; Shi, Dong-Yang. A Nonconforming Finite Element Method for Constrained Optimal Control Problems Governed by Parabolic Equations. Taiwanese J. Math. 21 (2017), no. 5, 1193--1211. doi:10.11650/tjm/7929. https://projecteuclid.org/euclid.twjm/1501599189


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