In this paper, we study a model for the magnetization in thin ferromagnetic films. It comes as a variational problem for $S^1$-valued maps $m^{\text{'}}$ (the magnetization) of two variables $x^{\text{'}}$: $E_{\epsilon }\left(m^{\text{'}}\right)=\epsilon \int {|{\nabla }^{\text{'}}·m^{\text{'}}|}^{2}d{x}^{\text{'}}+\frac{1}{2}\int {\left||{\nabla }^{\text{'}}{|}^{-1/2}{\nabla }^{\text{'}}·m^{\text{'}}\right|}^{2}d{x}^{\text{'}}$. We are interested in the behavior of minimizers as $\epsilon \to 0$. They are expected to be $S^1$-valued maps $m^{\text{'}}$ of vanishing distributional divergence ${\nabla }^{\text{'}}·m^{\text{'}}=0$, so that appropriate boundary conditions enforce line discontinuities. For finite $\epsilon >0$, these line discontinuities are approximated by smooth transition layers, the so-called Néel walls. Néel...

In this article, we derive a complete mathematical analysis of a coupled 1D-2D model for 2D wave propagation in media including thin slots. Our error estimates are illustrated by numerical results.