[Tuor Turambar,Cursed by the Valar]

Yes, as i said, elves can die in many of the ways humans can. Drowning, fire, poion, starvation, they all kill elves, because elves have the same basic needs humans have.

Also, it is possible that dying of a broken heart is actually refusing to eat until you die of starvation. Of course, i would not be suprised to see evidence to the contrary in one of the books i have not read.