[Mugwump]

See text below.

Then going to the House of the Kings in the Silent Street, Aragorn laid him down on the long bed that had been prepared for him. There he said farewell to Eldarion, and gave into his hands the winged crown of Gondor and sceptre of Arnor; and then all left him save Arwen, and she stood alone by his bed. And for all her wisdom and lineage she could not forbear to plead with him to stay yet for a while. She was not yet weary of her days, and thus she tasted the bitterness of the mortality that she had taken upon her.

"Lady Undómiel," said Aragorn, "the hour is indeed hard, yet it was made even in that day when we met under the white birches in the garden of Elrond, where none now walk. And on the hill of Cerin Amroth when we forsook both the Shadow and the Twilight this doom we accepted. Take counsel with yourself, beloved, and ask whether you would indeed have me wait until I wither and fall from my high seat unmanned and witless. Nay, lady, I am the last of the Númenoreans and the latest King of the Elder Days; and to me has been given not only a span thrice that of Men of Middle-earth, but also the grace to go at my will, and give back the gift. Now, therefore, I will sleep.

I speak no comfort to you, for there is no comfort for such pain within the circles of the world. the uttermost choice is before you: to repent and go to the Havens and bear away into the West the memory of our days together that shall there be evergreen but never more than a memory; or else to abide the Doom of Men."

"Nay, dear lord," she said, "that choice is long over. There is now no ship to bear me hence, and I must indeed abide the Doom of Men, whether I will or nill: the loss and the silence. But I say to you, King of the Númenoreans, not till now have I understood the tale of your people and their fall. As wicked fools I scorned them, but I pity them at last. For if this is indeed, as the Eldar say, the gift of the One to Men, it is bitter to receive."

"So it seems," he said. "But let us not be overthrown at the final test, who of old renounced the Shadow and the Ring. In sorrow we must go, but not in despair. Behold! We are not bound forever in the circles of the world, and beyond them is more than memory, Farewell!"

"Estel, Estel!" she cried, and with that even as he took her hand and kissed it, he fell into sleep. Then a great beauty was revealed in him, so that all who after came there looked on him with wonder; for they saw the grace of his youth, and the valor of his manhood, and the wisdom and majesty of his age were all blended together. And long there he lay, an image of the splendour of the Kings of Men in glory undimmed before the breaking of the world.

From The Tale of Aragorn and Arwen, LOTR, Appendix A.

We can see where Jackson got some of the dialogue between Elrond and Arwen!