Modeling chip formation is critical to any finite element approach depicting a metal-cutting process. The severe deformation within the chip, combined with immense strain rates in the primary, secondary, and tertiary deformation zones, fosters the development of distorted elements, yielding premature simulation termination. The Arbitrary Lagrangian-Eulerian (ALE) technique is an established method capable of pushing the limits toward a holistic representation of chip formation by reducing mesh distortion. Following this approach, the relevant part of the workpiece can be delimited by Eulerian, Lagrangian, or sliding surfaces, thus achieving model reduction. Nevertheless, in most cases, the standard adaptive mesh algorithm is ineffective in avoiding premature termination. This is particularly true if a non-constant chip thickness is to be simulated, such as in milling processes and in contrast to turning operations. An approach toward stabilizing the mesh quality in the chip formation zone has already been integrated into models and presented in the literature. These models have been validated via measured residual stresses on the tool rake face and by the engagement of instrumented end mills, measuring temperature online. The applied strategy is to impose kinematic ALE mesh constraints. In the workpiece, nodes of the adaptive mesh outside the process zone are pulled along, following the movement of the cutting tool edge. This ensures that there are always enough elements in the process zone. This strategy makes it possible to reproduce the kinematics of the milling process, i.e., the movement of the tool relative to the workpiece, for the first time, without transformations of the movement path or an artificial initial chip thickness. In this work, the strategy is expanded to include an essential benefit. An initial mesh pattern is defined depending on the process parameters. In addition, time-dependent ALE mesh constraints are used, which control the evolution of the mesh pattern by guiding nodes and associated elements into or out of the process zone, always ensuring mesh compatibility. The fact that the thickness of the chip root reduces as the investigated climb milling process progresses requires controlling the mesh pattern in the sense of a stable simulation. This work presents the new strategy, including its application with different tool geometries. The focus is on model-building and model-reduction aspects related to chip formation.