Stable and convergent unsymmetric meshless collocation methods

Leevan LING*, Robert Schaback

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

60 Citations (Scopus)

Abstract

In the theoretical part of this paper, we introduce a simplified proof technique for error bounds and convergence of a variation of Kansa's well-known unsymmetric meshless collocation method. For a numerical implementation of the convergent variation, a previously proposed greedy technique is coupled with linear optimization. This algorithm allows a fully adaptive on-the-fly data-dependent meshless selection of test and trial spaces. The new method satisfies the assumptions of the background theory, and numerical experiments demonstrate its stability.

Original languageEnglish
Pages (from-to)1097-1115
Number of pages19
JournalSIAM Journal on Numerical Analysis
Volume46
Issue number3
DOIs
Publication statusPublished - 2008

Scopus Subject Areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Convergence
  • Error bounds
  • Kansa's method
  • Linear optimization

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