Numerische Mathematik

, Volume 122, Issue 1, pp 101–131 | Cite as

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

  • Samuel Ferraz-LeiteEmail author
  • Jens Markus Melenk
  • Dirk Praetorius
Open Access


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 



S. Ferraz-Leite acknowledges a Grant of the graduate school “Differential Equations—Models in Science and Engineering”, funded by the Austrian Science Fund (FWF) under Grant W800-N05. The research of SFL and the last author DP is supported through the FWF project “Adaptive Boundary Element Method”, funded by the Austrian Science Fund (FWF) under Grant P21732.

Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.


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Copyright information

© The Author(s) 2012

Authors and Affiliations

  • Samuel Ferraz-Leite
    • 1
    Email author
  • 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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