Author： Townsend Alex Wendland Holger
Publisher： Oxford University Press
ISSN： 1464-3642
Source： IMA Journal of Numerical Analysis, Vol.33, Iss.3, 2013-07, pp. : 1095-1114
Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.
Abstract
Compactly supported radial basis functions can be used to define multiscale approximation spaces. A multiscale scheme is studied for the approximation of Sobolev functions on bounded domains with restricted data sites. Our method employs compactly supported radial basis functions with centres at scattered data sites chosen at each level to ensure the support of the interpolant is contained within the domain. The multiscale approximation is constructed by successive residual corrections at each level using support radii appropriate to capture different scales. Convergence for the scheme is proven and numerical examples are given.
Related content
A class of bounded operators on Sobolev spaces
By Korry S.
Archiv der Mathematik, Vol. 82, Iss. 1, 2004-01 ,pp. :
Access to resources
Recommend
Coarse grid spaces for domains with a complicated boundary
Numerical Algorithms, Vol. 21, Iss. 1-4, 1999-09 ,pp. :