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Journal of Scientific Computing

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16-09-2015

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

Authors: Yanping Chen, Fenglin Huang

Published in: Journal of Scientific Computing | Issue 1/2016

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Abstract

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.

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Title: Galerkin Spectral Approximation of Elliptic Optimal Control Problems with -Norm State Constraint
Authors: Yanping Chen
Fenglin Huang
Publication date: 16-09-2015
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 1/2016
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-015-0071-y

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