This is why you should never rely on silly simulation programs.
There are a few things wrong with that circuit:
U2 will go into drop out, you won't get 12V on the output but 10V at full load.
C1 is probably not large enough to avoid ripple.
You need to use a higher voltage transformer, I'd suggest 15V. The simulator doesn't simulate the transformer's series resistance or regulation factor so the output voltage will be higher with no load than when fully loaded. The sharp peaks drawn by the filter capacitor charging can cause the voltage to drop below the 16V, the minimum voltage required to keep the regulator regulating properly.