Journal Article

Multiscale methods with compactly supported radial basis functions for Galerkin approximation of elliptic PDEs

A. Chernih and Q. T. Le Gia

in IMA Journal of Numerical Analysis

Published on behalf of Institute of Mathematics and its Applications

Volume 34, issue 2, pages 569-591
Published in print April 2014 | ISSN: 0272-4979
Published online June 2013 | e-ISSN: 1464-3642 | DOI: http://dx.doi.org/10.1093/imanum/drt004
Multiscale methods with compactly supported radial basis functions for Galerkin approximation of elliptic PDEs

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The aim of this work is to consider multiscale algorithms for solving partial differential equations (PDEs) with Galerkin methods on bounded domains. We provide results on convergence and condition numbers. We show how to handle PDEs with Dirichlet boundary conditions. We also investigate convergence in terms of the mesh norms and the angles between subspaces to better understand the differences between the algorithms and the observed results. We also consider the issue of the supports of the radial basis funtions overlapping the boundary in our stability analysis, which has not been considered in the literature to the best of our knowledge.

Keywords: radial basis function; compact support; Galerkin approximation; partial differential equation; multiscale

Journal Article.  0 words. 

Subjects: Mathematics

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