Ground cover Identification please

This has been growing around trees around my house this spring and up against my house in some places. Now it has started gowning into my yard and I'm concerned that it might take over. I like it as ground cover but do not want it in my yard.

Every now and then I see some of the mature group of pants have small trumpet purple flowers on them. I have not see any now for a few weeks though.
At first I thought it might be some kind of Potentilla but i cant find any thing that looks just like it.

Here are 3 pictures i took of them growing outside and one on a CD that shows you the size of the individual plant.



can anyone help me identify this plant?
TYIA

 

here is one more picture to help.

 

Might be speedwell, Veronica persica
and I just installed Leopard a couple of days ago!

 

I dont see any vines it looks like it comes strait from the ground, and it seems to finger out under the ground.

Lepoard rocks :) been using it now for 6 months.

 

I think it may be a dwarf mallow can anyone verify this for me and tell me a good way to keep it out of my yard?

 

A flower will tell for sure.

 

Im sure its Ground Ivy — Glechoma hederacea .

http://www.msuturfweeds.net/details/_/ground_ivy_9/

that describes it to a T.

 

Possibly one of the dwarf Gunnera's. Try G.magellanica. Your ground ivy looks good too.