Is it useful/sensible to display a 'Refresh' button on a website's page (simple page, not dialog!), like the picture below?

First I thought it's a good idea, but know I start to think it's not so good, because the users should (?) know how to refresh their browser-pages (both desktop and mobile).
Or is it better to provide them more and more buttons to perform actions like a 'normal' application?
In this case the 'Refresh' button reloads the full page and not just some part of it.
refreshbutton, and the example that you give is in my opinion not justified either because technically that screen shouldn't exist. Perhaps your use-case in fact justifies a secondrefreshbutton. So that's why I say "it depends on the use-case". Can you describe your use-case a little better? – Bazzz Dec 20 '12 at 14:05