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

Source abstract

Recently, a new class of surface-divergence free radial basis function interpolants has been developed for surfaces in R 3 \mathbb {R}^3 . In this paper, several approximation results for this class of interpolants will be derived in the case of the sphere, S 2 \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.