Error and stability estimates for surface-divergence free RBF interpolants on the sphere Academic Article uri icon

abstract

  • Recently, a new class of surface-divergence free radial basis function interpolants has been developed for surfaces in R{double-struck}3. In this paper, several approximation results for this class of interpolants will be derived in the case of the sphere, S{double-struck}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. © 2009 American Mathematical Society.

author list (cited authors)

  • Fuselier, E. J., Narcowich, F. J., Ward, J. D., & Wright, G. B.

citation count

  • 11

publication date

  • January 2009