Free Access
Issue
ESAIM: M2AN
Volume 46, Number 4, July-August 2012
Page(s) 709 - 729
DOI https://doi.org/10.1051/m2an/2011052
Published online 03 February 2012
  1. A. Alonso and A. Valli, Eddy Current Approximation of Maxwell Equations : Theory, Algorithms and Applications. Springer (2010). [Google Scholar]
  2. C. Amrouche, C. Bernardi, M. Dauge and V. Girault, Vector potentials in three-dimensional non-smooth domains. Math. Methods Appl. Sci. 21 (1998) 823–864. [CrossRef] [MathSciNet] [Google Scholar]
  3. O. Bodart, A.V. Boureau and R. Touzani, Numerical investigation of optimal control of induction heating processes. Appl. Math. Modelling 25 (2001) 697–712. [CrossRef] [Google Scholar]
  4. F. Bonnans and A. Shapiro, Perturbation Analysis of Optimization Problems. Springer-Verlag, New York (2000). [Google Scholar]
  5. A. Bossavit and J.-F. Rodrigues, On the electromagnetic induction heating problem in bounded domains. Adv. Math. Sci. Appl. 4 (1994) 79–92. [Google Scholar]
  6. E. Casas, Pontryagin’s principle for state-constrained boundary control problems of semilinear parabolic equations. SIAM J. Control Optim. 35 (1997) 1297–1327. [CrossRef] [MathSciNet] [Google Scholar]
  7. S. Clain and R. Touzani, A two-dimensional stationary induction heating problem. Math. Methods Appl. Sci. 20 (1997) 759–766. [CrossRef] [Google Scholar]
  8. S. Clain, J. Rappaz, M. Swierkosz and R. Touzani, Numerical modelling of induction heating for two-dimensional geometries. Math. Models Methods Appl. Sci. 3 (1993) 805–7822. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  9. P.-E. Druet, O. Klein, J. Sprekels, F. Tröltzsch and I. Yousept, Optimal control of three-dimensional state-constrained induction heating problems with nonlocal radiation effects. SIAM J. Control Optim. 49 (2011) 1707–1736. [CrossRef] [MathSciNet] [Google Scholar]
  10. J.A. Griepentrog, Maximal regularity for nonsmooth parabolic problems in Sobolev-Morrey spaces. Adv. Differ. Equ. 12 (2007) 1031–1078. [Google Scholar]
  11. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman, Boston (1985). [Google Scholar]
  12. D. Hömberg, Induction hardening of steel – modeling, analysis and optimal design of inductors. Habilitation thesis, TU Berlin (2001). [Google Scholar]
  13. D. Hömberg, A mathematical model for induction hardening including mechanical effects. Nonlin. Anal. Real World Appl. 5 (2004) 55–90. [CrossRef] [Google Scholar]
  14. J.L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications. Dunod, Paris 1–3 (1968). [Google Scholar]
  15. A.C. Metaxas, Foundations of Electroheat : A Unified Approach. Wiley (1996). [Google Scholar]
  16. P. Monk, Finite element methods for Maxwell’s equations. Clarendon press, Oxford (2003). [Google Scholar]
  17. J.C. Nédélec, Mixed finite elements in R3. Numer. Math. 35 (1980) 315–341. [CrossRef] [MathSciNet] [Google Scholar]
  18. J. Nocedal and S.J. Wright, Numerical Optimization. Springer-Verlag, New York (1999). [Google Scholar]
  19. C. Parietti and J. Rappaz, A quasi-static two-dimensional induction heating problem. I : Modelling and analysis. Math. Models Methods Appl. Sci. 8 (1998) 1003–1021. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  20. C. Parietti and J. Rappaz, A quasi-static two-dimensional induction heating problem II. numerical analysis. Math. Models Methods Appl. Sci. 9 (1999) 1333–1350. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  21. J. Rappaz and M. Swierkosz, Mathematical modelling and numerical simulation of induction heating processes. Appl. Math. Comput. Sci. 6 (1996) 207–221. [Google Scholar]
  22. F. Tröltzsch, Optimal control of partial differential equations, Graduate Studies in Mathematics. American Mathematical Society, Providence, RI 112 (2010). [Google Scholar]
  23. D. Wachsmuth and A. Rösch, How to check numerically the sufficient optimality conditions for infinite-dimensional optimization problems, in Optimal control of coupled systems of partial differential equations, Internat. Ser. Numer. Math. Birkhäuser Verlag, Basel 158 (2009) 297–317. [Google Scholar]
  24. I. Yousept, Optimal control of a nonlinear coupled electromagnetic induction heating system with pointwise state constraints. Mathematics and its Applications/Annals of AOSR 2 (2010) 45–77. [Google Scholar]
  25. I. Yousept, Optimal control of Maxwell’s equations with regularized state constraints. Comput. Optim. Appl. (2011) DOI: 10.1007/s10589-011-9422-2. [Google Scholar]

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