A319 Captain reported aircraft reverted to Alternate Law during cruise. While continuing to destination airport; aircraft returned to Normal Law but experienced a yaw damper failure during descent.

Narrative

While in cruise at FL350 we received an ECAM for F-CTL/ALTN LAW (PROT LOST). We followed ECAM procedures along with referencing the Flight Manual section X.XX.X (F/CTL ALTN LAW).ECAM procedures called for limiting Max Speed to 320 KT; along with applying Flap 3 landing procedures. Hydraulic Systems as well as ELACs; SECs and FACs appeared normal on system pages.We contacted Dispatch on VHF #2. They patched in Maintenance Control. We discussed continuing to ZZZ or diverting to ZZZ1; in addition to seeking any additional Maintenance guidance. After running the Non-Normal Landing Distance Table we decided to continue to ZZZ. Dispatch double checked our math and were in agreement. We informed Dispatch we would [request priority handling] for additional Safety margin on ATC constraints in addition to any additional F/CTL failures that might arise. We had received the aircraft from the ZZZ2 hangar where previous F/CTL write ups were recently addressed.I informed the Flight Attendants of our degraded state; our intention to continue to ZZZ and that we would not be notifying the passengers at that point.While around 10;000 feet descending into ZZZ the aircraft returned to Normal Law. We decided to proceed with a Flaps 3 landing as planned in case we lost Normal Law again.Around 5;000 feet I kicked off the autopilot. Shortly after doing so we received another ECAM for YAW Damper 1 Fail. There were no to Dos so we cleared the ECAM and Status messages while on downwind to [Runway] XX.We were vectored to an ILS for XX and landed. We exited at intersection 1 in ZZZ and taxied to gate XX uneventfully. Once at the gate we spoke with the Mechanics. Provided them with copies of the ELB reports. We discussed the Aircraft state with the next crew. I contacted our Dispatcher along with the Chief Pilot to verify they did not need anything else from us at that time.