Abstract
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.
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Acknowledgments
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.
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Ferraz-Leite, S., Melenk, J.M. & Praetorius, D. Numerical quadratic energy minimization bound to convex constraints in thin-film micromagnetics. Numer. Math. 122, 101–131 (2012). https://doi.org/10.1007/s00211-012-0454-z
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DOI: https://doi.org/10.1007/s00211-012-0454-z