"Above" is an adverb in #1. In your sentences, you are saying that the discussion is above something. However, it is implied that you are referring to wherever your sentence is:
Considering the discussion above (the body of text in which this sentence is located), we aim to provide a wrapper construction method…
(In that example, "above" is being used as a preposition.)
Obviously, you would never say that, but that is the meaning you're trying to convey. In response to the question of which is more common, I would say #2. Either is correct, but #2 sounds more formal.