My group wrapped up a campaign where there was initally a big gap in levels between two sets of players. We had two "old hands" who got in at the campaign's inception, and we had three (later four) "newbies" who had to start at 1st level when the campaign was already in full swing and the oldsters were about 5th level or so.
As one of those level 1 players, I did not think that it was going to be any fun, given the level disparity. But to my surprise, it worked out just great -- mostly due to excellent DM'ing. Instead of making us newbies face a bunch of CR 5 critters, where we would have been totally overmatched, he instead tailored the encounters so that the party faced critters and situations more appropriate to the lower levels characters in the party. Yet even when facing these "mooks" our higher-level oldsters were having to constantly have their bacon saved by us newbies. Maybe because we were that much more fragile, we played a bit more conservatively, and thus we were fresher for the "end game" of an encounter. Plus, us newbies earned XP far quicker than the oldsters, due to the nature of the XP awards table. We leveled faster and experienced far more character growth in the same amount of time relative to the oldsters.
In your particular case, I would think that the gaming experience of a level 12 person should not be too different than that of a level 14 or even 15 person. That gap is not so huge as to be unmanageable.