How do I approach a postdoc interview when my background is not same as the professor's?
My background is in computational mechanics, so I have some background to answer your question. It seems to me that you and the professor would make a good research team because your research interests and experience are complementary. Do not assume that the professor wants you to work on weak forms and model formulation. S/he might want to go in a more applied direction as @astronot said. Instead of assuming that the professor wants to produce more papers like s/he has done in the past, ask in the interview what you'd be expected to do.
Second, it might also be useful for you to learn weak forms, just like it might be useful for someone with a mathematical background to learn applied stuff using commercial packages.