FEM

I know the following: In linear FE analysis with linear constitutive law, say CST, there will not be any discontinuity across the adjacent (or neighboring) elements, for any of the fields---displacements, strains or stresses. But I do have certain questions that are not very well addressed in the introductory FEM texts:

(i) Assuming a displacement-based formulation, under what conditions would you expect discontinuities (or inter-element banding) to possibly appear in: (a) stresses? (b) strains? (c) displacements?

Finite Difference Method (FDM) and the related techniques such as FVM, are often found put to great use in fluid mechanics. See any simulation showing not only streamlines but also vortex shedding, turbulent mixing, etc.