How effective is mobic (meloxicam) in reducing swelling of the knee joint that causes pain in ostoarthritis?

Not much: While we often give "antiinflammatories" like candy to control pain and inflammation, the medications have only a very small affect on swelling. The majority of the benefits of the antiinflammatories are the pain-relieving aspects. They also have almost no affect on swelling inside the knee from osteoarthritis. Most of the fluid occurs from mechanical wear or bleeding within the joint.