Learn English – Inverse word order

I don't do "correct", but I find 3 to be the most natural, 2 acceptable, and 1 something that no native English speaker would say.

Incidentally I find the comma after please rather awkward and foreign-sounding.

Structurally, the phrase "here used method" is very similar to (for example) the phrase "previously cited example." Both "here used" and "previously cited" can function as modifiers before a noun or after it (as with "method here used" or "method used here" in the first case, and with "example previously cited" or "example cited previously" in the second). Nevertheless, most people, I think, would read "previously cited example" with much less effort than "here used method."

The difference is a matter of modifier recognition. In cases where the modifier (such as "here used") rarely appears before the noun it modifies, readers may be brought to a halt when they see it in that unaccustomed position. They are likely to have an easier time recognizing and comprehending the example you cite (unlike my counterexample) if the modifier appears after the noun and in the order "method used here" than if it appears in either of the other two orders considered here.

You can help readers grasp the intended connection in such situations by hyphenating the modifier when it appears before the noun, yielding constructions such as "the here-used method" and "the here-investigated case." Though the word order may still seem less than optimal, at least some readers will find the relationship of here and used to each other and to method easier to apprehend.