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We extend the recent rigorous convergence result of Abels and the secondauthor (arXiv preprint 2105.08434) concerning convergence rates for solutionsof the Allen-Cahn equation with a nonlinear Robin boundary condition towardsevolution by mean curvature flow with constant contact angle. More precisely,in the present work we manage to remove the perturbative assumption on thecontact angle being close to ninety degree. We establish under usualdouble-well type assumptions on the potential and for a certain class ofboundary energy densities the sub-optimal convergence rate of order$\smash{\varepsilon^{\frac{1}{2}}}$ for general contact angles $\alpha \in(0,\pi)$. For a very specific form of the boundary energy density, we evenobtain from our methods a sharp convergence rate of order $\varepsilon$; againfor general contact angles $\alpha \in (0,\pi)$.  Our proof deviates from the popular strategy based on rigorous asymptoticexpansions and stability estimates for the linearized Allen-Cahn operator.Instead, we follow the recent approach by Fischer, Laux and Simon (SIAM J.Math. Anal. 52, 2020), thus relying on a relative entropy technique. We developa careful adaptation of their approach in order to encode the constant contactangle condition. In fact, we perform this task at the level of the notion ofgradient flow calibrations. This concept was recently introduced in the contextof weak-strong uniqueness for multiphase mean curvature flow by Fischer, Laux,Simon and the first author (arXiv preprint 2003.05478).

Convergence rates for the Allen-Cahn equation with boundary contact energy: The non-perturbative regime