A posteriori error estimates with point sources in fractional sobolev spaces

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. (c) 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1018-1042, 2017