*Eva Longoria and Tony Parker, the sadly separating couple, met for lunch Wednesday afternoon at Shutters on the Beach (restaurant) in Santa Monica and according to a source, they only talked about the divorce. But folks are saying the two were looking pretty civil and quite friendly at their “meeting.”

“Eva and Tony were acting really lovey-dovey with each other. She was stroking his head with her hand. They did not look like a couple that has just filed for divorce,” says E! Online’s eyewitness (see tmz *photo above) . Meanwhile, People’s source says, “They remain friends and everything is amicable. Eva is a class act. That’s how gracious she is.”

Although fans and folks are hopeful the two will reconcile their differences, a source told US magazine they just met to work out the details of the divorce.

Longoria filed the dreaded papers after a long (3 years) strained marriage of alleged infidelity. She had enough of it after she allegedly found out Parker was having an affair with NBA player, Brent Barry’s wife.

*(See more photos from Tony and Eva’s lunch encounter here.)