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C. Carstensen, D. Praetorius:
"Numerical Analysis for a Macroscopic Model in Micromagnetics";
SIAM Journal on Numerical Analysis, 42 (2005), 6; 2633 - 2651.

The macroscopic behaviour of stationary micromagnetic phenomena
can be modelled by a relaxed version of the Landau-Lifshitz
minimization problem. In the limit of large and soft magnets
$\Omega$, it is reasonable to exclude the exchange energy and
convexify the remaining energy densities. The numerical analysis
of the resulting minimization problem
\begin{align*}
\min E_0^{**}(\m)
\text{ amongst }\m:\Omega\to\R^d
\text{ with } |\m(x)|\le1 \text{ for a.e. }x\in\Omega,
\end{align*}
for $d=2,3$, faces difficulties caused by the pointwise
side-constraint $|\m|\le1$ and an integral over the whole
space $\R^d$ for the stray field energy. This paper involves
a penalty method to model the side-constraint and reformulates
the exterior Maxwell equation via a nonlocal integral operator
$\PP$ acting on functions exclusively defined on $\Omega$. The
discretization with piecewise constant discrete magnetizations
leads to edge-oriented boundary integrals. The implementation
of which and related numerical quadrature is discussed as well
as adaptive algorithms for automatic mesh-refinement.A~priori
and a~posteriori error estimates provide a thorough rigorous
error control of certain quantities. Three classes of numerical
experiments study the penalization, empirical convergence rates,
and the performance of the uniform and adaptive mesh-refining
algorithms.

http://www.anum.tuwien.ac.at/~dirk/download/published/ccdpr02_sinum42.pdf