Phase field modeling is used in various areas of physics for solving problems involving moving interfaces. In solids, moving interfaces of interest can be cracks, damage, or grain boundaries. Instead of tracking the evolution of sharp interface in a domain (for example, the propagation of a crack), phase field models use regularization techniques to represent sharp interfaces with a diffuse order parameter that varies smoothly over the whole domain. The phase field regularization introduces an internal length scale, lint, that recovers the sharp interface in the limit lint → 0. Therefore, the internal length scale in a phase field model essentially imposes a constraint on the maximum mesh size that can be used in the vicinity of a moving interface.