Minimal energy spherical splines on Clough-Tocher triangulations for Hermite interpolation
The authors address the problem of Hermite interpolation, with a Hermite interpolating spherical spline, based on the Clough-Tocher triangular macro-elements problem which can be used in the estimation of the geo-potential near the surface of the Earth. The minimal energy interpolation method is used, the existence and uniqueness of the minimal energy spherical splines, satisfying Hermite interpolation conditions, being studied. It is proved that the approximation error of a given sufficiently smooth function by the minimal energy Hermite interpolating spline depends on the mesh size of the underlying triangulation cubically. Also, the equivalence between the energy functional minimizers related to different homogeneous extensions is shown in the sense that they all converge to the sampled functions, the order of convergence being independent of the extensions. Some numerical experiments are also done to complete the paper.
scientific article; zbMATH DE number 6055242