### Stabilization methods in relaxed micromagnetism

The magnetization of a ferromagnetic sample solves a non-convex variational problem, where its relaxation by convexifying the energy density resolves relevant macroscopic information. The numerical analysis of the relaxed model has to deal with a constrained convex but degenerated, nonlocal energy functional in mixed formulation for magnetic potential $u$ and magnetization $\mathbf{m}$. In [C. Carstensen and A. Prohl, Numer. Math. 90 (2001) 65–99], the conforming $P1-{\left(P0\right)}^{d}$-element in $d=2,3$ spatial dimensions is shown to...