More generally, a k-form that has been integrated over each k-dimensional cell (edges in 1D,
faces in 2D, etc.) is called a discrete differential k-form. (If you ever find the distinction confusing,
you might find it helpful to substitute the word “integrated” for the word “discrete.”) In practice,
however, not every discrete differential form has to originate from a continuous one—for instance,
a bunch of arbitrary values assigned to each edge of a mesh is a perfectly good discrete 1-form.