Department of Mathematics
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.
Kansa’s method, convergence, error bounds, linear optimization
Source Publication Title
SIAM Journal on Numerical Analysis
Society for Industrial and Applied Mathematics
Ling, L., and Robert Schaback. "Stable and convergent unsymmetric meshless collocation methods." SIAM Journal on Numerical Analysis 46.3 (2008): 1097-1115.