Results on meshless collocation techniques

Though the technique introduced by Kansa is very successful in engineering applications, there were no proven results so far on the unsymmetric meshless collocation method for solving PDE boundary value problems in strong form. While the original method cannot be proven to be fail-safe in general, we prove asymptotic feasibility for a generalized variant using separated trial and test spaces. Furthermore, a greedy variation of this technique is provided, allowing a fully adaptive matrix-free and data-dependent meshless selection of the test and trial spaces.