brand new oven heat element gone bad. my fault or faulty oven?
You mention 3 pole 4 conductor so you have peaked my interest. 

Further these ovens do not just work from a temperature sensor to say the oven is this hot turn it off now - there is also a safety thermostat - no logic just hard wired - it would turn off the oven. So you would need two separate systems to fail. 

This leads me to conclude that something was not quite right in your connection, or you had a real catastrophic issue with the oven (1 in 100 million type event) - the thermal cutoff sensor had to fail, the controller itself for temperature control had to fail - two entirely separate systems.

You do not show the oven model number or how you connected those wires (picture of oven connection) - this would help that we could know for sure how you connected it. If you were to post a picture of your connection and provide the model of your oven it would be helpful.

People make mistakes when hooking these ranges up because L1,L2, N and Ground are hooked up and also the link bar between N and Ground on a range needs to be removed or installed depending on the outlet configuration (not the socket - just because it has 4 poles does not mean it is connected that way - check it to know for sure) - it is possible for people to not remove the link bar when hooking up a 4 wire cable. 

You should not assume that the outlet itself is wired correctly, check the outlet first make sure it is a 4 wire and also that L1,L2,N , G exist to the proper prong connections correctly. 

Of course with out checking all of this - the possibility is you might burn up the new one that is coming..