Numerische Mathematik

, Volume 122, Issue 1, pp 101–131

Numerical quadratic energy minimization bound to convex constraints in thin-film micromagnetics

  • Samuel Ferraz-Leite
  • Jens Markus Melenk
  • Dirk Praetorius
Open Access

DOI: 10.1007/s00211-012-0454-z

Cite this article as:
Ferraz-Leite, S., Melenk, J.M. & Praetorius, D. Numer. Math. (2012) 122: 101. doi:10.1007/s00211-012-0454-z


We analyze the reduced model for thin-film devices in stationary micromagnetics proposed in DeSimone et al. (R Soc Lond Proc Ser A Math Phys Eng Sci 457(2016):2983–2991, 2001). We introduce an appropriate functional analytic framework and prove well-posedness of the model in that setting. The scheme for the numerical approximation of solutions consists of two ingredients: The energy space is discretized in a conforming way using Raviart–Thomas finite elements; the non-linear but convex side constraint is treated with a penalty method. This strategy yields a convergent sequence of approximations as discretization and penalty parameter vanish. The proof generalizes to a large class of minimization problems and is of interest beyond the scope of thin-film micromagnetics.

Mathematics Subject Classification (2010)

65K05 65K15 49M20 
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Copyright information

© The Author(s) 2012

Authors and Affiliations

  • Samuel Ferraz-Leite
    • 1
  • Jens Markus Melenk
    • 2
  • Dirk Praetorius
    • 2
  1. 1.Max-Planck-Institute for Mathematics in the SciencesLeipzigGermany
  2. 2.Vienna University of TechnologyViennaAustria

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