Stabilization of a degenerate minimization problem with the simple-layer potential

Samuel Ferraz-Leite

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Submission date: 13. Dec. 2011
Pages: 10
published in: Numerical Mathematics and Advanced Applications 2011 : Proceedings of ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester, September 2011 / A. Cangiani (ed.)
Berlin : Springer, 2013. - P. 101 - 109 
DOI number (of the published article): 10.1007/978-3-642-33134-3_11
Bibtex
with the following different title: Stabilization of a degenerate minimization problem with the single-layer potential
MSC-Numbers: 65K10, 65K15, 49M20
Keywords and phrases: thin-film micromagnetics, simple-layer potential, convex optimization, stabilization
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Abstract:
We consider the reduced model for thin-film devices in stationary micromagnetics proposed in [DeSimone, Kohn, Müller, Otto, Schäfer 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, Melenk, Praetorius 2011] 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.