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S. Ferraz-Leite, J. Melenk, D. Praetorius:
"Numerical quadratic energy minimization bound to convex constraints in thin-film micromagnetics";
Numerische Mathematik, 122 (2012), 1; 101 - 131.

We analyze the reduced model for thin-film devices in stationary
micromagnetics proposed in [DeSimone, Kohn, M¨uller, Otto, Schäfer
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. Numerical
experiments support our findings and illustrate the performance of
the proposed algorithm.

http://dx.doi.org/10.1007/s00211-012-0454-z