A321 pilot reported systems loss complicated the approach to landing. The Pilot reported that maintenance found a triple failure of the FMS system was caused by the complete failure of the FMC.

Narrative

Clear VFR conditions. ZZZZZ1 arrival into ZZZ at FL200 given clearance to descend to 15000 feet by ZZZZZ2. I entered 15000 ft. as a constraint on the FMS and immediately we got a CAB PR LDG ELEV FAULT ECAM message and an OFFSIDE FMS CONTROL on the ND. The AP1 decoupled from NAV mode without any warning or indication and reverted to HDG mode. ECAM procedure said to check landing elevation. Altimeters were set on 29.64 for field setting and landing elevation knob was set to AUTO. Quick Reference Handbook (QRH) had no additional procedures. Captain (CA) FMS was locked and no key selections or line selects would result in any change on FMS display. We alerted ATC to our NAV failure and requested vectors. We transferred controls to the First Officer (FO). We selected AP2 and regained NAV mode. We also determined that the CA ND was visible if the range was set to the same as the FO. We accomplished the Descent checklist and loaded and confirmed the RNAV GPS XXR. We asked for and received an extended vector to final with approach. Upon matching ND range with a good display on the CA side we transferred controls back to the CA. The aircraft was configured for landing between ZZZZZ3 and ZZZZZ4 and was fully configured and stable by ZZZZZ4. Crosswind was approximately 330/25 at around 1000 ft. with a substantial crab and reported by Tower to be 330/9 at the runway. Aircraft was stable at 1000 ft. Approaching the minimums of 520 ft.; I disconnected the Autopilot (AP) and the managed speed bug ran away and the auto-thrust surged causing the aircraft to get high and fast. The FO reached up and dialed back the speed on the Fuel Control Unit (FCU) which reduced thrust and I continued the approach making an aggressive correction to regain the glide path. This caused our speed to be excessive and our glide path to become steep below 500 ft. I had to make an immediate decision to continue or go around and I quickly decided to continue with the unknown system degradation as long as I had glide path on the VASI and the speed/thrust was not erratic. We touched down with a minor bounce and exited the runway at taxiway T. Upon touchdown; all of the ND and PFD and lower ECAM started flashing and flickering in all of the message/mode locations. We called for maintenance to meet us at the gate because we had no idea what we had as a problem. Upon talking with the mechanics we were informed that there was a triple failure within the FMS and that the mechanic had never seen that before. He indicated an FMGCU (Flight Management Guidance Control Unit) failure. The post flight maintenance report indicated a CAB PR LDG ELEV FAULT and a NAV LS TUNING DISAGREE. System degradation from the time of failure when entering /15000 ft. at ZZZZZ2 on the arrival up to and including screen flickering and flashing at touchdown was a complete unknown. I would like to see this failure researched and possibly considered for a safety bulletin. The weather conditions were such that it was relatively easy to recover from the deviation that occurred at AP disconnect; but in IMC it would have been more challenging.