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

We analyze the reduced model for thin-film devices in stationary micromagnetics proposed in [7, DeSimone, Kohn, Müller, 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.