Abstract
Spherical radial basis functions are used to define approximate solutions to strongly elliptic pseudodifferential equations on the unit sphere. These equations arise from geodesy. The approximate solutions are found by the Galerkin and collocation methods. A salient feature of the paper is a unified theory for error analysis of both approximation methods.
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Acknowledgments
The authors would like to thank Dr. Thong Le Gia for providing some parts of the code which are used in the numerical experiments. The first author is supported by the University International Postgraduate Award offered by the University of New South Wales. The second author is partially supported by the grant FRG PS17166.
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Pham, T.D., Tran, T. Strongly elliptic pseudodifferential equations on the sphere with radial basis functions. Numer. Math. 128, 589–614 (2014). https://doi.org/10.1007/s00211-014-0614-4
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DOI: https://doi.org/10.1007/s00211-014-0614-4