A posteriori error estimates of hp spectral element methods for integral state constrained elliptic optimal control problems

In this paper, we investigate the hp spectral element approximation for optimal control problem governed by elliptic equation with an integral constraint for state. We first present the optimality conditions of the continuous and discretized control problems, respectively. Then, hp a posteriori erro...

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Bibliographic Details
Published in:Applied numerical mathematics 2019-10, Vol.144, p.42-58
Main Authors: Chen, Yanping, Zhang, Jinling, Huang, Yunqing, Xu, Yeqing
Format: Article
Language:English
Subjects:
A posteriori error estimates
Elliptic equations
hp spectral element methods
Integral state constraint
Optimal control
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Summary:In this paper, we investigate the hp spectral element approximation for optimal control problem governed by elliptic equation with an integral constraint for state. We first present the optimality conditions of the continuous and discretized control problems, respectively. Then, hp a posteriori error estimates are obtained for the coupled state and control approximation. In the end, we use a simple and yet efficient projection algorithm to carry out ample numerical experiments which confirm our analytical results.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2019.05.015