Minimal energy spherical splines on Clough-Tocher triangulations for Hermite interpolation
- 作者：V. Baramidze V-Baramidze@wiu.edu
- 关键词：Clough&ndash ; Tocher macro-element ; Spherical Hermite interpolation ; Energy minimization
- 刊名：Applied Numerical Mathematics
- 出版年：2012
- 期刊代码：8_01689274
- 类别：cp
- 出版时间：September, 2012
- 卷：62
- 期：9
- 页码：1077-1088
- 文件大小：208 K
摘要
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 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.