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Numerical Solutions of a Boundary Value Problem on the Sphere Using Radial Basis Functions

  • Quoc T. Le Gia
Chapter

Abstract

Boundary value problems on the unit sphere arise naturally in geophysics and oceanography when scientists model a physical quantity on large scales. Robust numerical methods play an important role in solving these problems. In this article, we construct numerical solutions to a boundary value problem defined on a spherical sub-domain (with a sufficiently smooth boundary) using radial basis functions (RBFs). The error analysis between the exact solution and the approximation is provided. Numerical experiments are presented to confirm theoretical estimates.

Notes

Acknowledgements

The author is grateful to many helpful discussions with Dr. Kerstin Hesse when writing the earlier version of the paper. He would also like to thank Professor Francis Narcowich for pointing out the recent results on Sobolev bounds for functions with scattered zeros on a Riemannian manifold. Many helpful comments from the referees to improve the presentation of the paper are also acknowledged.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of New South WalesSydneyAustralia

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