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

Published online by Cambridge University Press:  19 September 2016

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:[email protected] (T. L. Hou), [email protected] (L. Li)
*Corresponding author. Email:[email protected] (T. L. Hou), [email protected] (L. Li)
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Abstract

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 L2 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.

Type
Research Article
Copyright
Copyright © Global-Science Press 2016 

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