Highly localized RBF Lagrange functions for finite difference methods on spheres

The aim of this paper is to show how rapidly decaying RBF Lagrange functions on the sphere can be used to create a numerically feasible, stable finite difference method based on radial basis functions (an RBF-FD-like method). For certain classes of PDEs this approach leads to rigorous convergence es...

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Bibliographic Details
Published in:BIT 2024-06, Vol.64 (2), Article 16
Main Authors: Erb, W., Hangelbroek, T., Narcowich, F. J., Rieger, C., Ward, J. D.
Format: Article
Language:English
Subjects:
Computational Mathematics and Numerical Analysis
Fineness
Finite difference method
Mathematical analysis
Mathematics
Mathematics and Statistics
Numeric Computing
Radial basis function
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Summary:The aim of this paper is to show how rapidly decaying RBF Lagrange functions on the sphere can be used to create a numerically feasible, stable finite difference method based on radial basis functions (an RBF-FD-like method). For certain classes of PDEs this approach leads to rigorous convergence estimates for stencils which grow moderately with increasing discretization fineness.
ISSN:0006-3835
1572-9125
DOI:10.1007/s10543-024-01016-x