In the Silmarilion the fact that Tinuviel gave up her immortality is mentioned. She could not do it by her own but only by asking the valar to do it, and by that sacrifice Beren has returned from the dead...
In the movie(I am not sure that it also appears in the book), Arwen tells Aragorn that she will give up her elvish "doom" - immortality, for staying with him in Middle Earth(at least that what I understood).
I have two questions:
1. Did it happen also in the book? if it did, where?
2. Can she give up her immortality by her own decision, without asking the Valar?