How does +elemental damage work?

Solution 1:

Elemental gems only affect the weapon they are in, by adding flat damage, and that would increase the DPS of that particular weapon but not of anything else (e.g. other weapons or skills). If you find any enchant that says +% to all poison damage, that would apply to everything. Most of those tend to be for armor, not weapons though.

If you look under arcane stats you can get an idea of what stats apply per weapon and which ones apply for all attack. For example, elemental damage % bonus is listed as a global stat, as are things like execute chance and critical chance. However, elemental flat damage and attack speed are listed under each separate weapon (hand).