Robustness of error estimates for phase field models at a class of topological changes

A priori and a posteriori error estimates for the numerical approximation of phase field models with a polynomial dependence on the inverse of the interface width as long as no topological changes occur have recently been derived. Numerical experiments show that they remain robust when topological changes of the interface take place. Based on an asymptotic expansion a lower bound for the principal eigenvalue of the linearized Allen-Cahn operator near a generic singularity is derived which explains this experimental observation.