Goal-Oriented Adaptivity in Control Constrained Optimal Control of Partial Differential Equations

Dual-weighted goal-oriented error estimates for a class of pointwise control constrained optimal control problems for second order elliptic partial differential equations are derived. It is demonstrated that the constraints give rise to a primal-dual weighted error term representing the mismatch in...

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Bibliographic Details
Published in:SIAM journal on control and optimization 2008-01, Vol.47 (4), p.1721-1743
Main Authors: Hintermüller, M., Hoppe, R. H. W.
Format: Article
Language:English
Subjects:
Applied mathematics
Estimates
Lagrange multiplier
Partial differential equations
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Summary:Dual-weighted goal-oriented error estimates for a class of pointwise control constrained optimal control problems for second order elliptic partial differential equations are derived. It is demonstrated that the constraints give rise to a primal-dual weighted error term representing the mismatch in the complementarity system due to discretization. The paper also contains a posteriori error estimators for the $L^2$-norm of the error in the state and in the adjoint state.
ISSN:0363-0129
1095-7138
DOI:10.1137/070683891