Journal of Optimization Theory and Applications

, Volume 154, Issue 3, pp 879–903 | Cite as

Finite Element Analysis of an Optimal Control Problem in the Coefficients of Time-Harmonic Eddy Current Equations



This paper is concerned with an optimal control problem governed by time-harmonic eddy current equations on a Lipschitz polyhedral domain. The controls are given by scalar functions entering in the coefficients of the curl-curl differential operator in the state equation. We present a mathematical analysis of the optimal control problem, including sensitivity analysis, regularity results, existence of an optimal control, and optimality conditions. Based on these results, we study the finite element analysis of the optimal control problem. Here, the state is discretized by the lowest order edge elements of Nédélec’s first family, and the control is discretized by continuous piecewise linear elements. Our main findings are convergence results of the finite element discretization (without a rate).


Optimal control with PDEs Eddy current equations Control in coefficients Nédélec’s curl-conforming edge elements 


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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Institut für MathematikTechnische Universität BerlinBerlinGermany

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