question on a topic from the book

[Voralphion]

but I know that the sons of Elrond chose to be mortal

Where does it say that they chose to be mortal. It says they remained with Celeborn in Rivendell for a while but it doesn't mention any thing about their choice.
Celeborn probably remained because he wasn't yet weary of middle earth and wanted to stay a while. After a bit though he became weary and so he sailed west.