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

DOI10.1016/j.apnum.2008.12.033zbMath1176.65147OpenAlexW1969287581MaRDI QIDQ842949

N. E. Zubov

Publication date: 28 September 2009

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2008.12.033

zbMATH Keywords

numerical experimentssphereboundary integral equationradial basis functionspherical basis function

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Boundary element methods for boundary value problems involving PDEs (65N38)

Related Items (10)

A mixed method for Dirichlet problems with radial basis functions ⋮ Solution to the Neumann problem exterior to a prolate spheroid by radial basis functions ⋮ A posteriori error estimates for hypersingular integral equation on spheres with spherical splines ⋮ Radial basis functions for the solution of hypersingular operators on open surfaces ⋮ Solving the heat equation on the unit sphere via Laplace transforms and radial basis functions ⋮ Strongly elliptic pseudodifferential equations on the sphere with radial basis functions ⋮ A direct boundary integral equation method for the numerical construction of harmonic functions in three-dimensional layered domains containing a cavity ⋮ Solving non-strongly elliptic pseudodifferential equations on a sphere using radial basis functions ⋮ Preconditioners for pseudodifferential equations on the sphere with radial basis functions ⋮ Adjusted sparse tensor product spectral Galerkin method for solving pseudodifferential equations on the sphere with random input data

Cites Work

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• Continuous and discrete least-squares approximation by radial basis functions on spheres
• Approximation on the sphere using radial basis functions plus polynomials
• Linear integral equations.
• Distributing many points on a sphere
• Spherical harmonics
• Optimal lower bounds for cubature error on the sphere \(S^2\)
• Positive definite functions on spheres
• Strictly Positive Definite Functions on Spheres
• Improved error bounds for scattered data interpolation by radial basis functions
• Scattered Data Interpolation on Spheres: Error Estimates and Locally Supported Basis Functions
• A necessary and sufficient condition for strictly positive definite functions on spheres
• Scattered Data Approximation

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