Elliot was shot in the arm in court by Kyle Ackerman. Olivia was visiting him at the hospital
Olivia: Did anyone call Kathy yet?
Elliot: No. Don't.
Olivia: Elliot. Don't be like that-
Elliot: She started divorce proceedings
Elliot: A couple of weeks ago. I have the papers at home, I just haven't signed them yet.
Note: It would take midway into season 8 for Elliot to sign the divorce papers