Who buries Arwen?

I've always felt sad about Arwen's death also, that she dies ("lays herself to rest")alone at Cerin Amroth, choosing to return to the place where she and Aragorn were betrothed, rather than stay with her family and eventually be buried with Aragorn. She says farewell to her children, so perhaps they knew where she was going, especially as the story survived "in the South" (i.e. Gondor) to be recorded and passed down. Tolkien tells us in the Appendix that "there is her green grave," so I take it to be a an actual grave or burial place.