  We describe and test numerically an adaptive meshless generalized finite
difference method based on radial basis functions that competes well with the
finite element method on standard benchmark problems with reentrant corners of
the boundary, sharp peaks and rapid oscillations in the neighborhood of an
isolated point. This is achieved thanks to significant improvements introduced
into the earlier algorithms of [Oleg Davydov and Dang~Thi Oanh, Adaptive
meshless centers and RBF stencils for Poisson equation, Journal of
Computational Physics, 230:287--304, 2011], including a new error indicator of
Zienkiewicz-Zhu type.
