  We present an algorithm for $hp$-adaptive collocation-based mesh-free
numerical analysis of partial differential equations. Our solution procedure
follows a well-established iterative solve-estimate-mark-refine paradigm. The
solve phase relies on the Radial Basis Function-generated Finite Differences
(RBF-FD) using point clouds generated by advancing front node positioning
algorithm that supports variable node density. In the estimate phase, we
introduce an Implicit-Explicit (IMEX) error indicator, which assumes that the
error relates to the difference between the implicitly obtained solution (from
the solve phase) and a local explicit re-evaluation of the PDE at hand using a
higher order approximation. Based on the IMEX error indicator, the modified
Texas Three Step marking strategy is used to mark the computational nodes for
$h$-, $p$- or $hp$-(de-)refinement. Finally, in the refine phase, nodes are
repositioned and the order of the method is locally redefined using the
variable order of the augmenting monomials according to the instructions from
the mark phase.
  The performance of the introduced $hp$-adaptive method is first investigated
on a two-dimensional Peak problem and further applied to two- and
three-dimensional contact problems. We show that the proposed IMEX error
indicator adequately captures the global behaviour of the error in all cases
considered and that the proposed $hp$-adaptive solution procedure significantly
outperforms the non-adaptive approach. The proposed $hp$-adaptive method stands
for another important step towards a fully autonomous numerical method capable
of solving complex problems in realistic geometries without the user
intervention.
