According to the Books, after Aragorn's death, Arwen says goodbye to her children, and then goes to Lothlorien. There, after wandering around a bit, she comes to Cerin Amroth, the hill where she and Aragorn pledged their love to each other, and died (presumably of a broken heart, or just old age, since she was now human). Since she had given up the "Life of the Eldar," she would probably meet Aragorn in the place where the Edain go after death.
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But Melkor also was there, and he came to the house of Fëanor, and there he slew Finwë King of the Noldor before his doors, and spilled the first blood in the Blessed Realm; for Finwë alone had not fled from the horror of the Dark.
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