Hi everybody. I am new to the thread. Please read below, it seems to be a definite solution to the battery drain issue after installing Jelly Bean 4.1.2.
A few days ago I installed the update (Jelly Bean 4.1.2) to my Samsung Galaxy 3. After the installation, my battery was going down like crazy. I did not want to go through the process of doing a hard reset, so I did something very simple which I first read in another forum. I used the phone until the battery was completely discharged, that is until the phone switched off by itself. After the device turned off automatically, I pressed the on button to make sure that I could not turn on the phone - in other words I wanted to make sure that the battery was completely discharged.
Then I charged the phone until the green light indicated that the battery was 100% charged. I unplugged the charger without turning on the phone, waited for about 10 minutes and then I plugged in the charger again. I noticed that the led turned red, indicating that the phone was again charging. I charged until the led went back to green (that is for about 10 min, but it might be better to charge longer, maybe for an hour). I unplugged the charger, I turned on the phone and the battery life went back to normal after that. It now discharges at about 1.2% per hour - I am happy with that.
Please follow the above process. It should work with everybody who has a problem with battery life after the Jelly Bean 4.1.2 update. I am not a tech guy, but it might have something to do with battery memory or something like that.
I hope I helped. If yes, please spread this solution to this and other forums.