Recently, a new class of surface-divergence free radial basis function interpolants has been developed for surfaces in R3. In this paper, several approximation results for this class of interpolants will be derived in the case of the sphere, S2. 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.
Fuselier, Edward J.; Narcowich, Francis J.; Ward, Joseph D.; and Wright, Grady. (2009). "Error and Stability Estimates for Surface-Divergence Free RBF Interpolants on the Sphere". Mathematics of Computation, 78(268), 2157-2186. http://dx.doi.org/10.1090/S0025-5718-09-02214-5