  We consider Poisson's equation with a finite number of weighted Dirac masses
as a source term, together with its discretization by means of conforming
finite elements. For the error in fractional Sobolev spaces, we propose
residual-type a posteriori estimators with a specifically tailored oscillation
and show that, on two-dimensional polygonal domains, they are reliable and
locally efficient. In numerical tests, their use in an adaptive algorithm leads
to optimal error decay rates.
