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 $𝐦$. 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...

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 m. In [C. Carstensen and A. Prohl, Numer. Math.90 (2001) 65–99], the conforming P1 - (P0)d-element in d=2,3 spatial dimensions...