A note on the meshless method using radial basis functions

Authors:
Yong Duan
Affiliations:
School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu 610054, PR China
Venue:
Computers & Mathematics with Applications
Year:
2008

Citing 12
Cited 1

On some techniques for approximating boundary conditions in the finite element method

Modelling 94 Proceedings of the 1994 international symposium on Mathematical modelling and computational methods
Error estimates for interpolation by compactly supported radial basis functions of minimal degree

Journal of Approximation Theory
Improved error bounds for scattered data interpolation by radial basis functions

Mathematics of Computation
Meshless Galerkin methods using radial basis functions

Mathematics of Computation
On unsymmetric collocation by radial basis functions

Applied Mathematics and Computation
Finite Element Method for Elliptic Problems

Finite Element Method for Elliptic Problems
A Particle-Partition of Unity Method for the Solution of Elliptic, Parabolic, and Hyperbolic PDEs

SIAM Journal on Scientific Computing
Fast Solution of the Radial Basis Function Interpolation Equations: Domain Decomposition Methods

SIAM Journal on Scientific Computing
Overlapping domain decomposition method by radial basis functions

Applied Numerical Mathematics
Radial Basis Functions

Radial Basis Functions
A meshless Galerkin method for Dirichlet problems using radial basis functions

Journal of Computational and Applied Mathematics
Preconditioning for radial basis functions with domain decomposition methods

Mathematical and Computer Modelling: An International Journal

A radial basis function method for solving PDE-constrained optimization problems

Numerical Algorithms

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Abstract

In this paper, we prove some inverse inequalities for the finite dimensional subspace interpolated by radial basis functions. The properties of these inequalities are worse than those in finite element spaces. These bad properties result in a huge condition number for both the collocation method and Galerkin method using radial basis functions. As applications, theoretical estimates of the condition numbers of a meshless method using radial basis functions are given.