Changing research topic
First, negative results are useful too: for instance if you can show that the method is inapplicable by trying every reasonable option to make it work, this is a result by itself and it might be worth publication. Since your intuition is that this method cannot work, why not try to prove it? It doesn't really matter that your supervisor doesn't share this intuition.

It's not very surprising that your supervisor insists on continuing in this direction since it was what you agreed to at the start. Now if this is not something you want to do, then you have no choice: you need to talk to them about switching to a different topic. Mind that it's not always feasible to switch to a completely different topic during the course of a research internship.

Without knowing the details, my impression is that it's probably in your interest to finish the work that has been started rather than restart something from scratch (I assume that it's only for a few months). The important lesson here is: don't accept a topic that you don't like in the first place. Keep this in mind if you choose to do a PhD later ;)