L^2 norm equivalent a posteriori error estimate for a constrained optimal control problem
Liang Ge 1, Wenbin Liu 2, Danping Yang 31 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.
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: firstname.lastname@example.org, W.B.Liu@kent.ac.uk, email@example.com