Papers on the mathematical theory of meshless methods
Andrew Corrigan, John Wallin, and Thomas Wanner. A high order test discretization for unsymmetric meshless methods. January 2008. BibTeX arXiv
Abstract:
We introduce a high order test discretization for unsymmetric meshless methods, which samples the residual's derivatives in addition to the residual itself.
When modified to use this new test discretization, unsymmetric meshless methods can exploit arbitrarily high smoothness in the solution to obtain arbitrarily
high convergence orders or convergence in arbitrarily strong Sobolev norms, assuming a previously conjectured inverse inequality. This is justified using a new sampling inequality within the context of Schaback's
framework.