Convergence order estimates of meshless collocation methods using radial basis functions |
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Authors: | Franke Carsten Schaback Robert |
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Institution: | 1.Institut für Numerische und Angewandte Mathematik der Universität Göttingen, Lotzestraße 16-18, D-37083, Göttingen, Germany ; |
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Abstract: | We study meshless collocation methods using radial basis functions to approximate regular solutions of systems of equations
with linear differential or integral operators. Our method can be interpreted as one of the emerging meshless methods, cf.
T. Belytschko et al. (1996). Its range of application is not confined to elliptic problems. However, the application to the
boundary value problem for an elliptic operator, connected with an integral equation, is given as an example. Although the
method has been used for special cases for about ten years, cf. E.J. Kansa (1990), there are no error bounds known. We put
the main emphasis on detailed proofs of such error bounds, following the general outline described in C. Franke and R. Schaback
(preprint).
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | convergence orders meshless collocation radial basis functions partial differential equations 35A40 65N35 41A25 41A63 65R20 |
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