In this paper, we prove that solutions of the anisotropic Allen–Cahn equation in doubleobstacle form
![](//static.cambridge.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS0308210500023374/resource/name/S0308210500023374_eqnU1.gif?pub-status=live)
where A is a strictly convex function, homogeneous of degree two, converge to an anisotropic mean-curvature flow
![](//static.cambridge.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS0308210500023374/resource/name/S0308210500023374_eqnU2.gif?pub-status=live)
when this equation admits a smooth solution in ℝn. Here VN and R respectively denote the normal velocity and the second fundamental form of the interface, and
More precisely, we show that the Hausdorff-distance between the zero-level set of φ and the interface of the above anisotropic mean-curvature flow is of order O(ε2).