RBF Multiscale Collocation for Second Order Elliptic Boundary Value Problems

@article{Farrell2013RBFMC,
  title={RBF Multiscale Collocation for Second Order Elliptic Boundary Value Problems},
  author={Patricio Farrell and Holger Wendland},
  journal={SIAM J. Numer. Anal.},
  year={2013},
  volume={51},
  pages={2403-2425}
}
In this paper, we discuss multiscale radial basis function collocation methods for solving elliptic partial differential equations on bounded domains. The approximate solution is constructed in a multilevel fashion, each level using compactly supported radial basis functions of smaller scale on an increasingly fine mesh. On each level, standard symmetric collocation is employed. A convergence theory is given, which builds on recent theoretical advances for multiscale approximation using… 

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