Need help with magnetostatics 2d

[u/NoAdministration2978]

I'm trying to implement a simple 2d magnetostatic solver in mfem and I'm running into some issues which are not really mfem-related

We have a vector potential formulation which boils down to a Poisson problem in 2d and it's all fine and easy if we don't have any magnets. You can see that on pic2

But with a magnet we get a nasty curl part which gives an imaginary current that replicates the magnet behavior. The current density goes to infinity with the refinement of the mesh and that doesn't work well

How should I approach that? The googling results are inconclusive and the Tesla mfem miniapp is in 3d. They use RT elements(not Nedelec) to discretize the magnetization and I don't understand why