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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.

MSC:
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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