How could I convince my PhD adviser that the method, which is provided by him to me, does not work? I'm a PhD student in the US in the middle of my third year. We use a method for some simulations that is initially provided to me by my PhD adviser, despite the fact that all other research groups, that do the same simulation as us, use different method, which is a way more powerful than ours. Our method has really known limitation which makes it really difficult to get correct results comparable to other research groups that use other method. In fact, I should say nobody really used our method for these kind of simulations before.

I did a complete literature review and it turns out except a few research groups, that my adviser believes their works are bogus, nobody really used our method for this problem to get the correct results. In fact, those papers, which are bogus in my PhD adviser's opinion, are done behind the limitation of our method and that's the origin of his belief. But the problem is: professional research groups use other method, which does not have this limitation at all and as a result their works look more different in terms of final results.

In fact, my PhD adviser wants the results of other research groups but with our method, which looks impossible to me due to my three years experience on both of these methods and my comprehensive literature review. But still my PhD adviser believes it should be doable by our method. By the way my PhD adviser does not have any paper in the field of my PhD thesis and also did not know anything about this topic before I started my PhD.

In my opinion, if nobody use our method to do this research, it does not mean people are fool or idiot that does not know how to use our method. In fact, if there is not much literature about the application of our method in this particular problem, it means our method is awful for these kind of simulations (it's already known more or less in the literature but some people like my PhD adviser does not want to believe...). The problem is even by knowing that this method does not work and if even wants to work, takes 10 times more time and computational resource in comparison to other research groups, my PhD adviser still insists on to use this method and not to switch to the conventional method that other known researchers use to address our research questions.

I tried in several ways by bringing up the literature review and the work of other people and my works during these three years, but my PhD adviser keeps telling that: "I don't believe in those papers!".

I mean how someone could believe that we are the smartest people in the world that are trying to solve a problem with a wrong tool but so many other people who worked in this field more than two decades are fool that used other method to address this problem?! My question is: How can I convince my PhD adviser that we are just using a wrong tool and that's it. If we want to get correct results similar to the literature we should use their method? I really appreciate any suggestion or recommendation.
You are in your third PhD year and have done a thorough review of the state of the art. It seems your adviser cannot give you proper reasons for using the existing method and has no relevant papers in this field. This means you are the expert here. If you find the new method superior, then go ahead, implement it and use it. Of course, you have to invest time but eventually it will pay off as you can overcome certain limitations and your simulations will run faster. In the end it is your thesis and if you knowingly stick to a inferior method, you stay below what is possible.

Maybe you can even write a comparison of the two methods in terms of performance (if you are interested). If your adviser accepts the comparison result, then you can use your favourite method and get a first paper out of it.

If your adviser insists on using a method against all scientific proof, then it might be time for a change. Of course, a change of superviser or research group at this advanced stage of your PhD must be considered thoroughly and probably is the last resort.