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Numerical Methods for Constrained Elliptic Optimal Control Problems with Rapidly Oscillating Coefficients

Published online by Cambridge University Press:  28 May 2015

Yanping Chen and
Yuelong Tang
Yanping Chen*
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, Guangdong, China
Yuelong Tang
Affiliation:
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan, China
*
Corresponding author. Email: yanpingchen@scnu.edu.cn
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Abstract

In this paper we use two numerical methods to solve constrained optimal control problems governed by elliptic equations with rapidly oscillating coefficients: one is finite element method and the other is multiscale finite element method. We derive the convergence analysis for those two methods. Analytical results show that finite element method can not work when the parameter ε is small enough, while multiscale finite element method is useful for any parameter ε.

Keywords

65K0565K1065M60Optimal control problemsfinite element methodmultiscale finite element methodhomogenizationconvergence analysis

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Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 1 , Issue 3 , August 2011, pp. 235 - 247
Copyright
Copyright © Global-Science Press 2011

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