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Error Estimates of Mixed Methods for Optimal Control Problems Governed by General Elliptic Equations

Part of:Existence theoriesPartial differential equations, boundary value problems

Published online by Cambridge University Press:  19 September 2016

Tianliang Hou and
Li Li
Tianliang Hou*
Affiliation:
School of Mathematics and Statistics, Beihua University, Jilin 132013, China
Li Li*
Affiliation:
Key Laboratory for Nonlinear Science and System Structure, School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404100, China
*
*Corresponding author. Email:htlchb@163.com (T. L. Hou), zyxlily81@126.com (L. Li)
*Corresponding author. Email:htlchb@163.com (T. L. Hou), zyxlily81@126.com (L. Li)

Abstract

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In this paper, we investigate the error estimates of mixed finite element methods for optimal control problems governed by general elliptic equations. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. We derive L 2 and H –1-error estimates both for the control variable and the state variables. Finally, a numerical example is given to demonstrate the theoretical results.

Keywords

General elliptic equationsoptimal control problemssuperconvergenceerror estimatesmixed finite element methods

MSC classification

Secondary:49J20: Optimal control problems involving partial differential equations65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

Information

Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 6 , December 2016, pp. 1050 - 1071
Copyright
Copyright © Global-Science Press 2016 

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