I agree with oerkelens’ answer but I am surprised no one has mentioned that the expected form, at least in British English, would normally be “our meeting today”. I believe I have answered a few questions but I guess I’m going to have to repeat my own reply later. What follows is David Morrison’s welcome to the PSU today. At best, “If our today’s meeting are not for our day, the correct idiom is our meeting today, without any grammatical arguments and I think most of the grammatical arguments are valid, then why is it not true?