Thanks, everyone, for their replies. I checked out the different flowers you named, as well as the great website with flower pics (have that one in my favorites now).

The flowers you have named are not the same as what we are seeing. The petals of the smallish (1 inch) flowers we have are very pointed--it really looks like bright blue starfish growing along a vine-like stem among a sea of green serated ground cover.

Our neighbor has a similar patch growing along a rock wall, but they do not know what it is either. We haven't seen it anywhere else in the garden, so we don't think it's a weed. Hmmm, a garden mystery!

I have another one:

We have a large shrub (about 6 ft high) with large (3 inch) bright yellow blooms. The flowers cluster in threes, but open at different times. They each have 5 rounded petals, with a conical tube-like stamen jutting out from a yellow hairy center. The shrub is just now bursting with blossoms, but before it ever re-greened after winter, it had a spell of flowers in late winter. No scent to the flowers, and the shrub sends out runners along the bottom. Haven't been able to identify it in the usual manner.

We have plenty of mystery plants here...

All the best, Elektra UK