Many problems involve small parameters such that the limit problem is a practically good approximation. As examples we consider the thickness of a thin elastic structure, and the Knudson number (mean free path) in the Boltzmann Equation. The traditional way is to derive first a hierarchy of reduced models, which are then discretized. Our aim is to discretize directly the original equation. Typically, one of the discretization parameters can be reinterpreted as choice of the model.