Most cities I know have Park & Ride facilities at the outskirts near ring roads. Barcelona doesn't seem to have these (though perhaps I'm missing them as I don't own a car).
But I know my colleagues who come from outside are always struggling to find a parking spot, and they tell me there is no P&R.
Park & Ride is something that rarely makes economic sense. If you have a location with good public transport connections to the city, you probably want to build housing there. Alternate uses of the land – and parking in particular – are less valuable. Because people don't want to pay the market price for the land for parking, Park & Ride only works with heavy subsidies. The subsidies are usually implicit and implemented via zoning regulations, because taxpayers would revolt instantly against explicit subsidies.
It does work for tourists and other occasional visitors, but then the challenge is to make them aware it is an option when they plan the trip.