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S. Ferraz-Leite, J. Melenk, D. Praetorius:
"Numerical quadratic energy minimization bound to convex constraints in thin-film micromagnetics";
in: "ASC Report 32/2011", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2011, ISBN: 978-3-902627-04-9.

We analyze the reduced model for thin-film devices in stationary micromagnetics proposed in~\cite[DeSimone, Kohn, M\"uller, Otto, Sch\"afer 2001]{DeKoMuOtSc01}.
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.
Numerical experiments support our findings and illustrate the performance of the proposed algorithm.\\

http://www.asc.tuwien.ac.at/preprint/2011/asc32x2011.pdf