[The Squatter of Amon Rûdh]

This does raise an interesting question, though. Arwen did indeed have children, and although they had all long since come of age by the time Aragorn died, it does seem rather dismissive of them simply to disappear to fading Lothlórien and lie down to die, especially so soon after their father's death. Presumably they cared for her, and she for them; it's also likely that there was still a place for a Queen Mother in Gondor, possibly sometimes acting as advisor to her son, but the impression is that Arwen just gives up on life at her first bereavement.

The chances are that this just made for a better story, but it's an interesting thought. Perhaps having lived for all those centuries as an Elf has left Arwen unable to cope with the death of someone close to her (as is implicit in her final conversation with Aragorn).