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Int. J. Numer. Anal. Mod., 6 (2009), pp. 335-353. |
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L^2 norm equivalent a posteriori error estimate for a constrained optimal control problem Liang Ge 1, Wenbin Liu 2, Danping Yang 3 1 Department of Mathematics, Shandong University, Jinan, Shandong, 250100, China.2 KBS and IMS, University of Kent, Canterbury, CT2 7NF, England. 3 Department of Mathematics, East China Normal University, Shanghai, 200241, China. Received by the editors June 19, 2008. Abstract
Adaptive finite element approximation for a constrained optimal control problem is studied. A posteriori error estimators equivalent to the L^2 norm of the approximation error are derived both for the state and the control approximation, which are particularly suitable for an adaptive multi-mesh finite element scheme and applications where L^2 error is more important. The error estimators are then implemented and tested with promising numerical results. AMS subject classifications: 35R35, 49J40, 60G40 Key words: Convex optimal control problem, adaptive finite element method, L^2 norm equivalent a posteriori error estimate, multi-meshes. Email: geliangsdu@mail.sdu.edu.cn, W.B.Liu@kent.ac.uk, dpyang@math.ecnu.edu.cn |