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Talks and Poster Presentations (with Proceedings-Entry):

M. Aurada, J. Melenk, D. Praetorius:
"Mixed Conforming Elements for the Large-Body Limit in Micromagnetics (MATHMOD 09)";
Talk: 6th Vienna Conference on Mathematical Modelling, Wien; 02-11-2009 - 02-13-2009; in: "Proceedings MATHMOD 09 Vienna", I. Troch, F. Breitenecker (ed.); Argesim / Asim, ARGESIM Report no. 35 (2009), ISBN: 978-3-901608-35-3; 2296 - 2303.



English abstract:
The macroscopic behavior of stationary micromagnetic phenomena can be
modeled by a relaxed version of the Landau-Lifshitz minimization
problem first introduced by DESIMONE in 1993, where the magnetic
potential u is linked to the magnetizationmthrough the magnetostatic
Maxwell equation. In the case of large and soft magnets Ω, one
neglects the exchange energy and convexifies the remaining energy
densities. In our discretization we enforce the pointwise side
constraint |m| ≤ 1 by a penalization strategy and we replace the
entire space R^d in the energy functional E and in the potential
equation by a bounded Lipschitz domain ,Ω containing Ω. Since
conforming elements appear to be unstable for the pure Galerkin
discretization (cf. [Carstensen, Prohl 2001]) we append to the
Galerkin discretization a consistent stabilization term. We
reformulate the minimization problem in terms of the augmented
Lagrangean, which leads us to a so called saddle-point formulation
for the corresponding Euler-Lagrange equations. In this paper we
discuss the well-posedness of the discrete problem and the a priori
error analysis. Furthermore we introduce a residual-based a
posteriori error estimator and comment on adaptive strategies.


Electronic version of the publication:
http://www.asc.tuwien.ac.at/~dirk/download/published/amp_mathmod2009.pdf


Created from the Publication Database of the Vienna University of Technology.