Radial Basis Function Interpolation in Sobolev Spaces and Its Applications

Abstract

In this paper we study the method of interpolation by radial basis functions and give some error estimates in Sobolev space $H^k(\Omega)$ $(k \geq 1)$. With a special kind of radial basis function, we construct a basis in $H^k(\Omega)$ and derive a meshless method for solving elliptic partial differential equations. We also propose a method for computing the global data density.