S0025-5718-09-02207-8.pdf (220.83 kB)
Inf-sup condition for spherical polynomials and radial basis functions on spheres
journal contribution
posted on 2023-06-08, 05:08 authored by Ian H Sloan, Holger WendlandInterpolation 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
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- Published
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- Published version
Journal
Mathematics of ComputationISSN
0025-5718Publisher
American Mathematical SocietyIssue
267Volume
78Page range
1319-1331Department affiliated with
- Mathematics Publications
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- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2013-02-12First Open Access (FOA) Date
2013-02-12First Compliant Deposit (FCD) Date
2013-02-12Usage metrics
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