I think by the time of the LOTR there would have probably been no elven children in Rivendell. More likely in the silvan realms of Lorien and Mirkwood. The elves were fading, and as the burden of their years lay heavier on them they would have been unlikely to have inflicted it on others. It is likely that Arwen was one of the last elves born at RIvendell - hence the name Evenstar.
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“But Finrod walks with Finarfin his father beneath the trees in Eldamar.”
Christopher Tolkien, Requiescat in pace
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