  Local meshless methods using RBFs augmented with monomials have become
increasingly popular, due to the fact that they can be used to solve PDEs on
scattered node sets in a dimension-independent way, with the ability to easily
control the order of the method, but at a greater cost to execution time. We
analyze this ability on a Poisson problem with mixed boundary conditions in 1D,
2D and 3D, and reproduce theoretical convergence orders practically, also in a
dimension-independent manner, as demonstrated with a solution of Poisson's
equation in an irregular 4D domain. The results are further combined with
theoretical complexity analyses and with conforming execution time
measurements, into a study of accuracy vs. execution time trade-off for each
dimension. Optimal regimes of order for given target accuracy ranges are
extracted and presented, along with guidelines for generalization.
