Error and Stability Estimates for Surface-Divergence Free RBF Interpolants on the Sphere

Edward J. Fuselier; Francis J. Narcowich; Joseph D. Ward; Grady Wright

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

Error and Stability Estimates for Surface-Divergence Free RBF Interpolants on the Sphere

Edward J. Fuselier
, Francis J. Narcowich
, Joseph D. Ward
, Grady Wright

Mathematics Department

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

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Abstract

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.

Original language	American English
Pages (from-to)	2157-2186
Number of pages	30
Journal	Mathematics of Computation
Volume	78
Issue number	268
DOIs	https://doi.org/10.1090/S0025-5718-09-02214-5
State	Published - Oct 2009

Keywords

Incompressible fluids
Numerical modeling
Radial basis functions
Sphere
Stream function
Vector fields

EGS Disciplines

Mathematics

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10.1090/S0025-5718-09-02214-5

Error and Stability Estimates for Surface-Divergence Free RBF IntFinal published version, 485 KBLicense: Other

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title = "Error and Stability Estimates for Surface-Divergence Free RBF Interpolants on the Sphere",

abstract = " 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.",

keywords = "Incompressible fluids, Numerical modeling, Radial basis functions, Sphere, Stream function, Vector fields",

author = "Fuselier, \{Edward J.\} and Narcowich, \{Francis J.\} and Ward, \{Joseph D.\} and Grady Wright",

year = "2009",

month = oct,

doi = "10.1090/S0025-5718-09-02214-5",

language = "American English",

volume = "78",

pages = "2157--2186",

number = "268",

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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 - https://www.scopus.com/pages/publications/70349862230

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 -

Error and Stability Estimates for Surface-Divergence Free RBF Interpolants on the Sphere

Abstract

Keywords

EGS Disciplines

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