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21-05-2019 | Original Paper

A posteriori error estimates of hp spectral element methods for optimal control problems with L²-norm state constraint

Authors: Xiuxiu Lin, Yanping Chen, Yunqing Huang

Published in: Numerical Algorithms | Issue 3/2020

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Abstract

In this paper, we investigate a distributed optimal control problem governed by elliptic partial differential equations with L²-norm constraint on the state variable. Firstly, the control problem is approximated by hp spectral element methods, which combines the advantages of the finite element methods with spectral methods; then, the optimality conditions of continuous system and discrete system are presented, respectively. Next, hp a posteriori error estimates are derived for the coupled state and control approximation. In the end, a projection gradient iterative algorithm is given, which solves the optimal control problems efficiently. Numerical experiments are carried out to confirm that the numerical results are in good agreement with the theoretical results.

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Title: A posteriori error estimates of hp spectral element methods for optimal control problems with L2-norm state constraint
Authors: Xiuxiu Lin
Yanping Chen
Yunqing Huang
Publication date: 21-05-2019
Publisher: Springer US
Published in: Numerical Algorithms / Issue 3/2020
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI: https://doi.org/10.1007/s11075-019-00719-5

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