  The thin plate spline, as introduced by Duchon, interpolates a smooth surface
through scattered data. It is computationally expensive when there are many
data points. The finite element thin plate spline (TPSFEM) possesses similar
smoothing properties and is efficient for large data sets. Its efficiency is
further improved by adaptive refinement that adapts the precision of the finite
element grid. Adaptive refinement processes and error indicators developed for
partial differential equations may not apply to the TPSFEM as it incorporates
information about the scattered data. This additional information results in
features not evident in partial differential equations. An iterative adaptive
refinement process and five error indicators were adapted for the TPSFEM. We
give comprehensive depictions of the process in this article and evaluate the
error indicators through a numerical experiment with a model problem and two
bathymetric surveys in square and L-shaped domains.
