Document Type

Journal Article

Department/Unit

Department of Mathematics

Abstract

In the theoretical part of this paper, we introduce a simplified proof technique for error bounds and convergence of a variation of E. 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 onthe- 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.

Publication Year

2008

Journal Title

SIAM Journal on Numerical Analysis

Volume number

46

Issue number

3

Publisher

Society for Industrial and Applied Mathematics

First Page (page number)

1097

Last Page (page number)

1115

Referreed

1

ISSN (print)

00361429

Keywords

Kansa’s method, convergence, error bounds, linear optimization

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