Error and stability estimates for surface-divergence free RBF interpolants on the sphere

Fuselier, Edward; Narcowich, Francis; Ward, Joseph; Wright, Grady

doi:10.1090/S0025-5718-09-02214-5

Error and stability estimates for surface-divergence free RBF interpolants on the sphere
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by Edward J. Fuselier, Francis J. Narcowich, Joseph D. Ward and Grady B. Wright;

Math. Comp. 78 (2009), 2157-2186

DOI: https://doi.org/10.1090/S0025-5718-09-02214-5

Published electronically: January 22, 2009

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Abstract:

Recently, a new class of surface-divergence free radial basis function interpolants has been developed for surfaces in $\mathbb {R}^3$. In this paper, several approximation results for this class of interpolants will be derived in the case of the sphere, $\mathbb {S}^2$. In particular, Sobolev-type error estimates are obtained, as well as optimal stability estimates for the associated interpolation matrices. In addition, a Bernstein estimate and an inverse theorem are also derived. Numerical validation of the theoretical results is also given.

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