Garmin's elevation correction just ignores the altitude data from the device and calculates altitude using a US topo database that has data points every ten meters or so.
The barometric altimeter needs time to calibrate when you first turn the device on. This can take some time. So if you want to turn the device on and go, but still get accurate elevation you need to manually calibrate the altimeter.
Here is the Garmin FAQ on the topic:
Question: How accurate is the elevation on my Edge 500?
Answer:
The Edge 500 calculates elevation data using a barometric altimeter as opposed to satellite information. The standard area of accuracy for the device, when given time to calibrate, is +/- 50 feet. The barometric pressure sensor, which is responsible for altimeter readings, is not temperature compensated. Temperature changes in the measuring device will affect the barometric pressure sensor and altimeter readings
To ensure that elevation data is accurate at the beginning of an activity the user has the ability to calibrate the elevation manually. To calibrate the elevation manually, please follow the steps below.
1. Go to the Main Menu
2. Select GPS
3. Select Set Elevation
4. Set the elevation to the known elevation of your starting point
5. Select Save
The elevation will then be calibrated from this manually set elevation if your activity begins within thirty meters of the set elevation.