Tolkien drew from the same sources of mythology.
I don't think so. I think that Tolkien may have pulled from the mythology but Rowling is pulling from Tolkien. Doesn't matter, she has written six great stories. Can't wait for number seven.
Actually, according to some interviews I've read, and the documentary on Tolkien from the special edition FotR DVD set, Tolkien, a professor of languages, was depressed that other than Beowulf, Great Britan really doesn't have its own mythos, the originals having been displaces by conquerors, like the Normans. So he was interesting in coming up with a mythology for England. Of course, he did draw on other mythologies, but his main reason for coming up with middle earth was to give England a mythos.