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I don't think there is one http://www.adobe.com/products/photoshop-premiere-elements/tech-specs.html
Since PrElements does not do hardware acceleration like PrPro, a better question would be to post a brand/model here and ask if anyone has problems with that brand/model
I should have stated on a laptop computer.
Almost any ATI or nVidia graphics adapter with dedicated video ram will do well
An Intel "chip on the motherboard" graphics adapter will NOT do well since Intel does not update drivers very often
A laptop with DUAL graphics adapters will OFTEN cause problems... read below
Dual video problems (some for Premiere Pro, but the idea is the same)
-link to why http://forums.adobe.com/message/4685328
This is more about PrPro, but http://forums.adobe.com/thread/1369220?tstart=0 has ideas
Eula Foster Smith
A Premiere Elements user posted the following in one of the threads recently
As John has pointed out, the video card/graphics card in a Premiere Elements environment are not in the same league as those for Premiere Pro. For Premiere Elements, most NVIDIA and ATI cards appear to be popular and in use, provided the drivers kept up to date.
I have been working with Intel HD Graphics on Windows 7, 8, and 8.1 64 bit and have had no problems with Premiere Elements programs from 4 to 12 (laptop and desktop).