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C. Carstensen, D. Praetorius:
"Stabilization yields strong convergence of macroscopic magnetization vectors for micromagnetics without exchange energy";
Report for Institute for Applied and Numerical Analysis, ANUM Preprint 20/2004; 2004; 18 pages.

The convexified Landau-Lifshitz minimization problem in micromagnetics leads
to a degenerate variational problem. Therefore strong convergence of finite
element approximations cannot be expected in general.
This paper introduces a stabilized finite element discretization which allows
for the strong convergence of the discrete magnetization fields with reduced
convergence order for a uniaxial model problem. This yields a convergent
method for the approximation of the Young measure describing the
microstructure for the generalized solution of the non-relaxed Landau-Lifshitz
problem.

http://www.asc.tuwien.ac.at/~dirk/download/preprint/ccdpr6.pdf