Macbook Air hangs during Catalina 10.15.7 update

I tried to update my MacBook Air (early 2014) from Catalina 10.15.6 to 10.15.7. Not long after the Apple logo with the progress bar appear, there is no more progress. First time without any remaining time estimate, second time with 'Time remaining less than a minute'. This lasts hours and after about 3-4 hours, the MacBook switches itself off. After restart, it shows that the update has not been performed. Has somebody any idea how to proceed?