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The thin plate spline, as introduced by Duchon, interpolates a smooth surfacethrough scattered data. It is computationally expensive when there are manydata points. The finite element thin plate spline (TPSFEM) possesses similarsmoothing properties and is efficient for large data sets. Its efficiency isfurther improved by adaptive refinement that adapts the precision of the finiteelement grid. Adaptive refinement processes and error indicators developed forpartial differential equations may not apply to the TPSFEM as it incorporatesinformation about the scattered data. This additional information results infeatures not evident in partial differential equations. An iterative adaptiverefinement process and five error indicators were adapted for the TPSFEM. Wegive comprehensive depictions of the process in this article and evaluate theerror indicators through a numerical experiment with a model problem and twobathymetric surveys in square and L-shaped domains.

Data-based Adaptive Refinement of Finite Element Thin Plate Spline