A321 pilot reported dual flight management computer failure during cruise. Flight diverted and experienced two flat tires during landing.

Narrative

During cruise we encountered a dual fmgc failure. This resulted in us losing all map and gps data. We then were not able to identify our exact location and requested priority handling. We elected to divert to the closest large airport; ZZZ. We received vectors from ATC and were able to remain vfr in the descent. We were heavy as we hadn't burned enough fuel to be under our MLW. We looked through the QRH for relevant checklists and decided to focus on flying the plane. We ran the checklist for overweight landing and determined a flaps 3 landing was required. We landed safely in ZZZ. ZZZ weather had about a 15kt crosswind from the right. This made it necessary to use more braking on the left side to keep centerline. High altitude; overweight; flaps 3 are all contributing factors on an increased approach speed and braking effort to safely stop the aircraft. Once we landed I turned on the brake fans. The 1&2 brake fans were MEL'd thus no cooling was provided to that side. CFR (Crash Fire Rescue) checked the plane and said everything looked normal. We began taxiing in the aircraft. Once we were closer to the gate area; CFR notified us that our #1 tire had gone flat. We stopped the aircraft. We were then told the #2 tire had gone flat as well. We were then unable to continue taxiing and requested stairs and buses to unload the passengers to the terminal. Cause: The higher brake temperature could have [been] slightly mitigated with a longer roll out.