Brett, Charles, Dedner, Andreas and Elliott, Charles (2016) Optimal control of elliptic PDEs at points. IMA Journal of Numerical Analysis, 36 (3). pp. 1015-1050. doi:10.1093/imanum/drv040 ISSN 0272-4979.

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Abstract

We consider an elliptic optimal control problem where the objective functional contains evaluations of the state at a finite number of points. In particular, we use a fidelity term that encourages the state to take certain values at these points, which means that our problem is related to ones with state constraints at points. The analysis and numerical analysis differs from when the fidelity is in the L2-norm because we need the state space to embed into the space of continuous functions. In this paper, we discretize the problem using two different piecewise linear finite element methods. For each discretization we use two different approaches to prove a prioriL2-error estimates for the control. We discuss the differences between these methods and approaches, and present numerical results that agree with our analytical results.

Item Type:	Journal Article
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title:	IMA Journal of Numerical Analysis
Publisher:	Oxford University Press
ISSN:	0272-4979
Official Date:	2016
Dates:	Date Event 2016 Published 2015 Available
Volume:	36
Number:	3
Page Range:	pp. 1015-1050
DOI:	10.1093/imanum/drv040
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

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