public transport – Park and Ride in Copenhagen

We will be five adults staying in Copenhagen from Sunday 5 May in the evening to Wednesday 8 May in the morning. Parking in Copenhagen itself was very expensive, so I was looking for a solution that would allow us to park our car somewhere in the city of Copenhagen at a reasonable price for those few days and then travel by public transport.

I found a car park in Copenhagen, but its answers are quite old and have outdated links.

Is there an "official" Park and Ride solution to my problem? If not, are there affordable and low-traffic car parks near good public transport links to the city center?