Stabilisation yields strong convergence of macroscopic magnetisation vectors for micromagnetics without exchange energy

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.