Free Access
Volume 50, Number 1, January-February 2016
Page(s) 237 - 261
Published online 14 January 2016
  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. F. Brezzi, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers. Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge 8 (1974) 129–151. [Google Scholar]
  4. P. Ciarlet, Jr. and J. Zou, Fully discrete finite element approaches for time-dependent Maxwell’s equations. Numer. Math. 82 (1999) 193–219. [CrossRef] [MathSciNet] [Google Scholar]
  5. M. Costabel, A remark on the regularity of solutions of Maxwell’s equations on Lipschitz domains. Math. Methods Appl. Sci. 12 (1990) 365–368. [CrossRef] [Google Scholar]
  6. M. Costabel and M. Dauge, Singularities of electromagnetic fields in polyhedral domains. Arch. Rational Mech. Anal. 151 2000 221–276. [CrossRef] [MathSciNet] [Google Scholar]
  7. M. Costabel, M. Dauge and S. Nicaise, Singularities of Maxwell interface problems. ESAIM: M2AN 33 (1999) 627–649. [CrossRef] [EDP Sciences] [Google Scholar]
  8. 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]
  9. V. Girault and P. Raviart, Finite Element Methods for Navier-Stokes Equations. Springer-Verlag, Berlin (1986). [Google Scholar]
  10. M. Hintermüller, K. Ito and K. Kunisch, The primal-dual active set strategy as a semismooth Newton method. SIAM J. Optim. 13 (2003) 865–888. [CrossRef] [MathSciNet] [Google Scholar]
  11. M. Hintermüller, A. Laurain I. Yousept, Shape sensitivities for an inverse problem in magnetic induction tomography based on the eddy current model. Inverse Problems 31 (2015) 065006. [CrossRef] [MathSciNet] [Google Scholar]
  12. R.H.W. Hoppe and I. Yousept, Adaptive edge element approximation ofH(curl)-elliptic optimal control problems with control constraints. BIT 55 (2015) 255–277. [CrossRef] [MathSciNet] [Google Scholar]
  13. M. Kolmbauer and U. Langer, A robust preconditioned minres solver for distributed time-periodic eddy current optimal control problems. SIAM J. Scientific Comput. 34 (2012) B785–B809. [CrossRef] [Google Scholar]
  14. M. Kolmbauer and U. Langer, Efficient solvers for some classes of time-periodic eddy current optimal control problems. In vol. 45 of Numerical Solution of Partial Differential Equations: Theory, Algorithms, and Their Applications, edited by O.P. Iliev, S.D. Margenov, P.D Minev, P.S. Vassilevski and L.T Zikatanov. Springer New York (2013) 203–216. [Google Scholar]
  15. J.E. Lagnese and G. Leugering, Time domain decomposition in final value optimal control of the Maxwell system. A tribute to J.L. Lions. ESAIM: COCV 8 (2002) 775–799. [CrossRef] [EDP Sciences] [Google Scholar]
  16. R. Leis, Initial-boundary value problems in mathematical physics. B.G. Teubner, Stuttgart (1986). [Google Scholar]
  17. A. Logg, K.-A. Mardal, and G.N. Wells, Automated Solution of Differential Equations by the Finite Element Method. Springer, Boston (2012). [Google Scholar]
  18. P. Monk, An analysis of a mixed method for approximating Maxwell’s equations. SIAM J. Numer. Anal. 28 (1991) 1610–1634. [CrossRef] [MathSciNet] [Google Scholar]
  19. P. Monk, Finite element methods for Maxwell’s equations. Clarendon Press, Oxford (2003). [Google Scholar]
  20. J.C. Nédélec, Mixed finite elements in R3. Numer. Math. 35 (1980) 315–341. [CrossRef] [MathSciNet] [Google Scholar]
  21. S. Nicaise, S. Stingelin and F. Tröltzsch, On two optimal control problems for magnetic fields. Comput. Methods Appl. Math. 14 (2014) 555–573. [CrossRef] [MathSciNet] [Google Scholar]
  22. S. Nicaise, S. Stingelin and F. Tröltzsch, Optimal control of magnetic fields in flow measurement. Discrete Contin. Dyn. Systems 8 (2015) 579–605. [CrossRef] [MathSciNet] [Google Scholar]
  23. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, New York (1983). [Google Scholar]
  24. R. Picard, On the boundary value problems of electro- and magnetostatics. Proc. Roy. Soc. Edinburgh, Sect. A Math. 92 (1982) 165–174. [CrossRef] [Google Scholar]
  25. F. Tröltzsch, Optimal Control of Partial Differential Equations, Vol. 112 of Grad. Stud. Math. American Mathematical Society, Providence, RI (2010). [Google Scholar]
  26. F. Tröltzsch and I. Yousept, PDE-constrained optimization of time-dependent 3D electromagnetic induction heating by alternating voltages. ESAIM: M2AN 46 (2012) 709–729. [CrossRef] [EDP Sciences] [Google Scholar]
  27. M. Ulbrich, Semismooth Newton methods for operator equations in function spaces. SIAM J. Optim. 13 (2003) 805–842. [Google Scholar]
  28. N. Weck, Maxwell’s boundary value problem on Riemannian manifolds with nonsmooth boundaries. J. Math. Anal. Appl. 46 (1974) 410–437. [CrossRef] [Google Scholar]
  29. N. Weck, Exact boundary controllability of a Maxwell problem. SIAM J. Control Optim. 38 (2000) 736–750. [CrossRef] [MathSciNet] [Google Scholar]
  30. I. Yousept, Optimal bilinear control of eddy current equations with grad-div regularization. J. Numer. Math. 23 (2015) 81–98. [CrossRef] [MathSciNet] [Google Scholar]
  31. I. Yousept, Optimal control of a nonlinear coupled electromagnetic induction heating system with pointwise state constraints. Ann. Acad. Rom. Sci. Ser. Math. Appl. 2 (2010) 45–77. [MathSciNet] [Google Scholar]
  32. I. Yousept. Finite element analysis of an optimal control problem in the coefficients of time-harmonic Eddy current equations. J. Optim. Theory Appl. 154 (2012) 879–903. [Google Scholar]
  33. I. Yousept, Optimal control of Maxwell’s equations with regularized state constraints. Comput. Optim. Appl. 52 (2012) 559–581. [Google Scholar]
  34. I. Yousept, Optimal control of quasilinear H(curl)-elliptic partial differential equations in magnetostatic field problems. SIAM J. Control Optim. 51 (2013) 3624–3651. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you