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A priori error estimates for optimal control problems with pointwise constraints on the gradient of the state
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Ortner, Christoph and Wollner, W.. (2011) A priori error estimates for optimal control problems with pointwise constraints on the gradient of the state. Numerische Mathematik, Volume 118 (Number 3). pp. 587600. ISSN 0029599X

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Official URL: http://dx.doi.org/10.1007/s0021101103609
Abstract
We analyze a finite element approximation of an elliptic optimal control problem with pointwise bounds on the gradient of the state variable. We derive convergence rates if the control space is discretized implicitly by the state equation. In contrast to prior work we obtain these results directly from classical results for the W 1,∞error of the finite element projection, without using adjoint information. If the control space is discretized directly, we first prove a regularity result for the optimal control to control the approximation error, based on which we then obtain analogous convergence rates.
Item Type:  Journal Article  

Subjects:  Q Science > QA Mathematics  
Divisions:  Faculty of Science > Mathematics  
Library of Congress Subject Headings (LCSH):  Finite element method, Differential equations, Partial  
Journal or Publication Title:  Numerische Mathematik  
Publisher:  Springer  
ISSN:  0029599X  
Official Date:  July 2011  
Dates: 


Volume:  Volume 118  
Number:  Number 3  
Page Range:  pp. 587600  
Identifier:  10.1007/s0021101103609  
Status:  Peer Reviewed  
Publication Status:  Published  
Access rights to Published version:  Restricted or Subscription Access  
Funder:  Deutsche Forschungsgemeinschaft (DFG), Engineering and Physical Sciences Research Council (EPSRC)  
Grant number:  1253 (DFG)  
References:  [1] R. A. Adams and J. J. F. Fournier, Sobolev Spaces, vol. 140 of Pure and Applied Mathematics 

URI:  http://wrap.warwick.ac.uk/id/eprint/43914 
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