We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
84/2011
Stabilization of a degenerate minimization problem with the simple-layer potential
Samuel Ferraz-Leite
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/i> 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.
Stabilization of a degenerate minimization problem with the single-layer potential
In: Numerical Mathematics and Advanced Applications 2011 : Proceedings of ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester, September 2011 / Andrea Cangiani (ed.) Berlin : Springer, 2013. - pp. 101-109
