Stationary $p$-harmonic maps approaching planar singular harmonic maps to the circle

Given a bounded planar domain $\mathrm{\Omega }\subset {\mathbb{R}}^2$, we show that any singular harmonic map into the circle ${\mathbb{S}}^1$ corresponding to a topologically nondegenerate critical point of the renormalised energy in the sense of Bethuel, Brezis and Hélein is a limit of stationary $p$-harmonic maps for $p<2$ as $p\to 2$