Minimal energy spherical splines on Clough–Tocher triangulations for Hermite interpolation

We present a study of the minimal energy method applied to the Hermite interpolation problem over Clough–Tocher partitions on the unit sphere. A subset of spline coefficients is found by satisfying nodal interpolating conditions. The rest of the coefficients are found through energy minimization sub...

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Bibliographic Details
Published inApplied numerical mathematics Vol. 62; no. 9; pp. 1077 - 1088
Main Author Baramidze, V.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.09.2012
Subjects
Clough–Tocher macro-element
Energy minimization
Spherical Hermite interpolation
Spherical Hermite interpolation
Clough–Tocher macro-element
Energy minimization
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Summary:We present a study of the minimal energy method applied to the Hermite interpolation problem over Clough–Tocher partitions on the unit sphere. A subset of spline coefficients is found by satisfying nodal interpolating conditions. The rest of the coefficients are found through energy minimization subject to C1 conditions. We show that the error in approximation of a given sufficiently smooth function by the minimal energy Hermite interpolating spline depends on the mesh size of the underlying triangulation cubically. In addition, we prove that minimizers of energy functionals with different homogeneous extensions are equivalent in the sense that they all converge to the sampled function, and the order of convergence is independent of the extension. We conclude with numerical examples.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2011.06.008