I have run across such a sentence:
Yesterday I was ill, so I went to the doctor's.
What is the function of possessive here, that is doctor's?
This type of possessive is commonly used to refer to a particular shop, or something similar to a shop like a doctor's surgery or a dental clinic. The pattern being used is: [somebody's] [place] (e.g. butcher's shop) and the unnecessary [place] is often left off for brevity. You will often hear the following used:
I'm going to the: