  The popularity of local meshless methods in the field of numerical
simulations has increased greatly in recent years. This is mainly due to the
fact that they can operate on scattered nodes and that they allow a direct
control over the approximation order and basis functions. In this paper we
analyse two popular variants of local strong form meshless methods, namely the
radial basis function-generated finite differences (RBF-FD) using polyharmonic
splines (PHS) augmented with monomials, and the weighted least squares (WLS)
approach using only monomials. Our analysis focuses on the accuracy and
stability of the numerical solution computed on scattered nodes in a two- and
three-dimensional domain. We show that while the WLS variant is a better choice
when lower order approximations are sufficient, the RBF-FD variant exhibits a
more stable behavior and a higher accuracy of the numerical solution for higher
order approximations, but at the cost of higher computational complexity.
