Stabilization of a Degenerate Minimization Problem with the Single-Layer Potential

S. Ferraz-Leite ()
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S. Ferraz-Leite: Max Planck Institute for Mathematics in the Sciences

A chapter in Numerical Mathematics and Advanced Applications 2011, 2013, pp 101-109 from Springer

Abstract: Abstract We consider the reduced model for thin-film devices in stationary micromagnetics proposed in DeSimone et al. (R Soc Lond Proc A 457(2016):2983–2991, 2001). In the case of soft material, one of the energy contributions is negligible, and the problem becomes degenerate. The analysis and the numerical scheme recently developed in Ferraz-Leite et al. (Numer Math, Accepted for publication, 2012) are not satisfactory in this case. In the present work, we overcome the degeneracy and extend the numerical scheme by introducing a stabilizing energy term. Convergence of the method is established and a numerical experiment concludes the paper.

Keywords: Side Constraint; Degenerate Minimization; Ferromagnetic Film; Penalty Scheme; Minimum Norm Solution (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-33134-3_11

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DOI: 10.1007/978-3-642-33134-3_11

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