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Stable and convergent unsymmetric meshless collocation methods. (English) Zbl 1167.65059
Authors’ summary: In the theoretical part of this paper, we introduce a simplified proof technique for error bounds and convergence of a variation of E. J. Kansa’s well-known unsymmetric meshless collocation method [Comput. Math. Appl. 19, No. 8–9, 127–145 (1990; Zbl 0692.76003); ibid., 147–161 (1990; Zbl 0850.76048)]. 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.

65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
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