Yes, you can use Elgato Game Capture HD software to capture from various iOS devices, including an iPad, iPhone or iPod touch.

You will need a newer iOS device that is capable of outputting 720p or 1080p, and an HDMI adapter from Apple, like the Lightning Digital AV Adapter or Apple 30-pin Digital AV Adapter.

Select the type of iOS device you're using in the Capture Settings of the Elgato Game Capture HD software.

You can use both the original Elgato Game Capture HD hardware, as well as the newer Elgato Game Capture HD60.