Data-based Adaptive Refinement of Finite Element Thin Plate Spline
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The thin plate spline, as introduced by Duchon, interpolates a smooth surface through scattered data. It is computationally expensive when there is a large number of 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 (PDEs) may not apply to the TPSFEM that incorporates information about the scattered data. This additional information results in features not evident in PDEs. An iterative adaptive refinement process and four 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 two bathymetric surveys in square and L-shaped domains.
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