[Gorthaur the Cruel]

It seems that Arwen's death was more bitter than that of Luthien & Beren for both died together for the Silmaril hastened their end. Melian's lineage (particularly the women) seem to be full of sorrow. It is quite a surprise to me also that Arwen would leave her own children to muse her sorrows in the fading land of Lothlorien, but as many here have said, the memory of her choice was here (lorien). The memory of her people, her Grandmother, & her mother who passed over the sea. So it is only fitting that the finality of the consequences of her choice should befall in the place where it had been sealed. she would've died a bitter death if she stayed in Gondor. Atleast, her sorrows, in some measure were eased by the memory of Lothlorien, fading like her.