If the quest marker points to a door, no matter which side of it you're on, this usually means the target is in a completely different cell (ie, outside of Bleak Falls Barrow). What's happening is that the game knows the target is not in your current cell so it points towards a door that will lead you towards the cell it is in - this isn't always the fastest route but can lead through other cells instead of straight to the one where the target is.
I would hazard a guess that since the game is behaving like Arvel is in neither the Barrow nor the Sanctum that he has somehow gotten outside. This shouldn't happen so it is most likely a bug. Plus, if he was outside then the marker should point towards the entrance and exit of the barrow and sanctum, respectively, but the game is famous for not being able to do this very well.
You should be able to verify this by back-tracking where you came from and head back outside via the entrance you came in through. Then, check where the map marker is pointing. If it's back at Bleak Falls Barrow then, as IllusiveBrian said, he may have fallen through the floor where the door to the sanctum is. If not then he is elsewhere in the world; track him down, kill him, take the claw and never trust a Dunmer again.