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Higher Order Triangular Mixed Finite Element Methods for Semilinear Quadratic Optimal Control Problems

Published online by Cambridge University Press:  28 May 2015

Kang Deng ,
Yanping Chen  and
Zuliang Lu
Kang Deng*
Affiliation:
School of Mathematical Sciences, Hunan University of Science and Technology, Xiangtan 411201, P.R. China
Yanping Chen*
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, P.R. China
Zuliang Lu*
Affiliation:
College of Mathematics and Computer Sciences, Chongqing Three Gorges University, Chongqing 404000, P.R. China College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan 411105, P.R. China
*
Corresponding author.Email address:kdeng@hnust.edu.cn
Corresponding author.Email address:yanpingchen@scnu.edu.cn
Corresponding author.Email address:zulianglux@126.com
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Abstract

In this paper, we investigate a priori error estimates for the quadratic optimal control problems governed by semilinear elliptic partial differential equations using higher order triangular mixed finite element methods. The state and the co-state are approximated by the order k Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise polynomials of order k (k ≥ 0). A priori error estimates for the mixed finite element approximation of semilinear control problems are obtained. Finally, we present some numerical examples which confirm our theoretical results.

Keywords

49J2065N30a priori error estimatessemilinear optimal control problemshigher order triangular elementsmixed finite element methods
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 4 , Issue 2 , May 2011 , pp. 180 - 196
Copyright
Copyright © Global Science Press Limited 2011

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