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Finite Element Approximation of Semilinear Parabolic Optimal Control Problems

Published online by Cambridge University Press:  28 May 2015

Hongfei Fu  and
Hongxing Rui
Hongfei Fu*
Affiliation:
School of Mathematics and Computational Science, China University of Petroleum, Qingdao, 266555, China
Hongxing Rui*
Affiliation:
School of Mathematics, Shandong University, Jinan 250100, China
*
Corresponding author.Email address:hongfeifu@upc.edu.cn
Corresponding author.Email address:hxrui@sdu.edu.cn
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Abstract

In this paper, the finite element approximation of a class of semilinear parabolic optimal control problems with pointwise control constraint is studied. We discretize the state and co-state variables by piecewise linear continuous functions, and the control variable is approximated by piecewise constant functions or piecewise linear discontinuous functions. Some a priori error estimates are derived for both the control and state approximations. The convergence orders are also obtained.

Keywords

49J2065M60Finite element approximationsemilinear parabolic optimal controlpointwise control constrainta priori error estimates
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 4 , Issue 4 , November 2011 , pp. 489 - 504
Copyright
Copyright © Global Science Press Limited 2011

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