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

Sloan, Ian H and Wendland, Holger (2009) Inf-sup condition for spherical polynomials and radial basis functions on spheres. Mathematics of Computation, 78 (267). pp. 1319-1331. ISSN 0025-5718

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Abstract

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 differential 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 sufficiently small. We then use the inf-sup condition to derive a new error analysis for the hybrid interpolation scheme of Sloan and Sommariva

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Holger Wendland
Date Deposited: 12 Feb 2013 14:55
Last Modified: 07 Mar 2017 07:28
URI: http://sro.sussex.ac.uk/id/eprint/24276

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