TY - JOUR
T1 - Radial Basis Function Interpolation in Sobolev Spaces and Its Applications
AU - Manping Zhang
JO - Journal of Computational Mathematics
VL - 2
SP - 201
EP - 210
PY - 2007
DA - 2007/04
SN - 25
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8685.html
KW - Sobolev space, Radial basis function, Global data density, Meshless method.
AB - <p style="text-align: justify;">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.</p>