feigning contempt
Just one of the many "tools" that Elliot and Olivia use to get a confession out of a suspect is their little "contempt play", as I like to call it. It's basically the two of them pretend-fighting with each other. It doesn't happen a lot, but it has happened a couple times, and it works. Cragen even once said "That was almost too convincing", or something along those lines, after witnessing one of Elliot and Olivia's fake spats. The reason the two do this is to get a suspect, who they know is guilty, to confess to the crime he or she committed. Elliot and Olivia will give each other dirty looks, name call, and act very annoyed with each other. Then one of them will leave the room in a huff.After witnessing all of this, the suspect/perp probably thinks they can play it to their advantage and try to badmouth the absent detective to the own who is still in the room. They become a little easier and open up more. The one example that stands out to me is when Olivia left the box after she and Elliot had it out. The suspect in this case did not seem to think highly of women, so when Elliot sighs and goes "Women, can't live with 'em..." or something along those lines, the suspect believed that he and Elliot had something in common and that he could complain about it to Elliot, who would most likely understand. But what he talks about ends up being the information needed to convict him.
One might think that if two people are so easily able to pretend hating each other, then they really do hate each other. But I couldn't disagree more. I think the way that Olivia and Elliot band together (in this very unobvious way) to bring the criminal down shows just how in sync they are with each other's feelings and intuition. One could begin to provoke the other, and he/she would know that it is just an act, and go along with it perfectly. Their dedication to ensure justice is served makes Olivia and Elliot play so well with each other, even if they aren't playing nice.