MD-11
Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 70; Flight Crew Total 10000; Flight Crew Type 2000
Communication Breakdown; Situational Awareness
Aircraft Equipment Problem Critical; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Maintenance
Flight Crew Landed in Emergency Condition
Aircraft; Procedure
I was the First Officer operating from ZZZ to ZZZ1. The aircraft had just been in maintenance and had the #2 CADC (Central Air Data Computer) replaced.  Holding short of runway 26L for departure; the tower cleared us for takeoff.  At 80 Kts; my airspeed indicator begin to lag behind the Captains; and I made all further calls from his PFD. Once airborne the Captain called for positive rate; gear up.  Once I placed the handle in the UP position; my PFD was unreadable and several EICAS messages displayed.  The Captain lost his flight director; the auto throttles disengaged and he was flying raw data at this point in time.  The Captain flew the aircraft raw data and commenced a left hand turn to fly the SID.  The Captain asked me to tell ATC we need to level at 5000 ft. I pressed my CADC switch on the SIS panel which restored the Captains flight director and auto throttles.  He then called for flaps up; slats retract; after takeoff checklist.  I was then instructed to contact the company via JETCOM; as the SATCOM was not working.  Several attempts were made to contact dispatch with the JETCOM. Approximately 20 minutes after departure the SATCOM communications worked and the captain had a conversation with ZZZ1.  Once this conversation was completed the Captain told me to request FL310; and we're going to ZZZ1.  I stated my concerns; and followed his instructions and requested FL310 with ATC.  Unintentionally; the flight continued into RVSM airspace without advising ATC that we were now non-compliant with RVSM regulations.  Ultimately the aircraft climbed to FL370.  The flight continued uneventful to ZZZ1 and landed.
First Officer reported that their newly replaced CADC2 computer failed on departure. The Captain elected to continue to the destination.