TY - JOUR
T1 - Error and Stability Estimates for Surface-Divergence Free RBF Interpolants on the Sphere
AU - Fuselier, Edward J.
AU - Narcowich, Francis J.
AU - Ward, Joseph D.
AU - Wright, Grady
PY - 2009/10
Y1 - 2009/10
N2 - Recently, a new class of surface-divergence free radial basis function interpolants has been developed for surfaces in R 3 . In this paper, several approximation results for this class of interpolants will be derived in the case of the sphere, 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.
AB - Recently, a new class of surface-divergence free radial basis function interpolants has been developed for surfaces in R 3 . In this paper, several approximation results for this class of interpolants will be derived in the case of the sphere, 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.
KW - Incompressible fluids
KW - Numerical modeling
KW - Radial basis functions
KW - Sphere
KW - Stream function
KW - Vector fields
UR - http://www.scopus.com/inward/record.url?scp=70349862230&partnerID=8YFLogxK
UR - https://scholarworks.boisestate.edu/math_facpubs/12
U2 - 10.1090/S0025-5718-09-02214-5
DO - 10.1090/S0025-5718-09-02214-5
M3 - Article
SN - 0025-5718
VL - 78
SP - 2157
EP - 2186
JO - Mathematics of Computation
JF - Mathematics of Computation
IS - 268
ER -