dV = FunctionSpace(mesh, "DG", 0)
A = Function(dV)
I am running a time-dependent problem, so I need the value of A.vector()[2] for the next time step. I can directly print out the [2] value in series, but how can I find the value of the same index number ([2] in series) if I run the code in parallel?
As you are here considering a DG-0 function this is linked to the cell index of your problem.
If you create a mesh tag marking this cell in serial (say give it the number 55), you can write this meshfunction to file, and then read it in to dolfin in parallel, locate which process has the cell with this marker, and what local index it has.