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Journal of Numerical Mathematics

Editor-in-Chief: Hoppe, Ronald H. W. / Kuznetsov, Yuri

Managing Editor: Olshanskii, Maxim

Editorial Board: Benzi, Michele / Brenner, Susanne C. / Carstensen, Carsten / Dryja, M. / Feistauer, Miloslav / Glowinski, R. / Lazarov, Raytcho / Nataf, Frédéric / Neittaanmaki, P. / Bonito, Andrea / Quarteroni, Alfio / Guzman, Johnny / Rannacher, Rolf / Repin, Sergey I. / Shi, Zhong-ci / Tyrtyshnikov, Eugene E. / Zou, Jun / Simoncini, Valeria / Reusken, Arnold

IMPACT FACTOR 2018: 3.107

CiteScore 2018: 2.43

SCImago Journal Rank (SJR) 2018: 1.252
Source Normalized Impact per Paper (SNIP) 2018: 1.618

Mathematical Citation Quotient (MCQ) 2018: 1.13

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Volume 23, Issue 1


Optimal bilinear control of eddy current equations with grad–div regularization

Irwin Yousept
  • Corresponding author
  • Universität Duisburg-Essen, Fakultät für Mathematik, Thea-Leymann-Straße 9, D-45127 Essen, Germany.
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Published Online: 2015-08-07 | DOI: https://doi.org/10.1515/jnma-2015-0007


An optimal bilinear control problem governed by time-harmonic eddy current equations is considered to estimate the electric conductivity of a 3D bounded isotropic domain. The model problem is mainly complicated by the possible presence of non-conducting materials in the domain. We introduce an optimal control approach based on grad-div regularization and divergence penalization. The estimation for the electric conductivity obtained by solving the optimal control problem is allowed to be discontinuous. Here, no higher regularity property can be derived from the corresponding optimality conditions. We analyze the approach and present various numerical results exhibiting its numerical performance

Keywords: PDE-constrained optimization; identification problem; eddy current equations; discontinuous electric conductivity; grad-div regularization; divergence penalization

About the article

Received: 2012-08-06

Accepted: 2013-09-13

Published Online: 2015-08-07

Published in Print: 2015-03-01

Citation Information: Journal of Numerical Mathematics, Volume 23, Issue 1, Pages 81–98, ISSN (Online) 1569-3953, ISSN (Print) 1570-2820, DOI: https://doi.org/10.1515/jnma-2015-0007.

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