If you look at the “Review database status” page under “Upgrade and Migration” in SharePoint 2010 Central Administration, you may see a message in the status column that says something like “Database in compatibility range and an upgrade is recommended”. To do this you need to run the PowerShell command “Upgrade-SPContentDatabase but to do this you need to get the identity of each database you want to upgrade and run this command for each one. I have numerous clients that have more than one content db, and you may also want to upgrade the Central Admin databases too, so I have written a PowerShell function that takes in the Web Application and upgrades all databases attached to it:

Function UpgradeDatabases($webApp)
{
    $web = Get-SPWebApplication -Identity $webApp
    foreach($contentDB in $web.ContentDatabases)
    {
        Upgrade-SPContentDatabase -id $contentDB
    }
}

A pretty straight forward function. Below is the ps1 file.

Download UpgradeDatabases file

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