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Inf-sup condition for spherical polynomials and radial basis functions on spheres

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posted on 2023-06-08, 05:08 authored by Ian H Sloan, Holger Wendland
Interpolation by radial basis functions and interpolation by polynomials are both popular methods for function reconstruction from discrete data given on spheres. Recently, there has been an increasing interest in employing these function families together in hybrid schemes for scattered data modeling and the solution of partial di?erential equations on spheres. For the theoretical analysis of numerical methods for the associated discretized systems, a so-called inf-sup condition is crucial. In this paper, we derive such an inf-sup condition, and show that the constant in the infsup condition is independent of the polynomial degree and of the chosen point set, provided the mesh norm of the point set is su?ciently small. We then use the inf-sup condition to derive a new error analysis for the hybrid interpolation scheme of Sloan and Sommariva

History

Publication status

  • Published

File Version

  • Published version

Journal

Mathematics of Computation

ISSN

0025-5718

Publisher

American Mathematical Society

Issue

267

Volume

78

Page range

1319-1331

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2013-02-12

First Open Access (FOA) Date

2013-02-12

First Compliant Deposit (FCD) Date

2013-02-12

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