Journal of Scientific Computing

, Volume 67, Issue 1, pp 65–83 | Cite as

Galerkin Spectral Approximation of Elliptic Optimal Control Problems with \(H^1\)-Norm State Constraint



In this paper, we study an elliptic optimal control problem with \(H^1\)-norm state constraint. The control problem is approximated by the Galerkin spectral method, which can provide high-order accuracy and fast convergence rate. The optimality conditions and a priori error estimates are presented. A reliable a posteriori error estimator is investigated, which is helpful for developing adaptive strategy in the spectral method. Some numerical tests confirm the error estimates and illustrate the performance of the indicator.


Optimal control Elliptic equations State constraint Legendre polynomials Galerkin spectral method 



The authors are grateful to the referees for their helpful and profound comments and advices.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.School of Mathematical SciencesSouth China Normal UniversityGuangzhouChina

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