Boundary integral equations on the sphere with radial basis functions: error analysis

Authors:
T. Tran;Q. T. Le Gia;I. H. Sloan;E. P. Stephan
Affiliations:
School of Mathematics and Statistics, The University of New South Wales, Sydney 2052, Australia;School of Mathematics and Statistics, The University of New South Wales, Sydney 2052, Australia;School of Mathematics and Statistics, The University of New South Wales, Sydney 2052, Australia;Institut für Angewandte Mathematik, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
Venue:
Applied Numerical Mathematics
Year:
2009

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Abstract

Radial basis functions are used to define approximate solutions to boundary integral equations on the unit sphere. These equations arise from the integral reformulation of the Laplace equation in the exterior of the sphere, with given Dirichlet or Neumann data, and a vanishing condition at infinity. Error estimates are proved. Numerical results supporting the theoretical results are presented.