Good quality point sets and error estimates for moving least square approximations. (English) Zbl 1040.65034

The author discusses the construction of moving least square approximations. Error estimates in Sobolev spaces are given. It is discussed that the condition number of the star of nodes could be used as a good measure for the quality of the distribution of the nodes and patches.


65F20 Numerical solutions to overdetermined systems, pseudoinverses
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65F35 Numerical computation of matrix norms, conditioning, scaling
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[1] Touzot, G.; Nayroles, B.; Villon, P., Generalizing the finite element method: Diffuse approximation and diffuse elements, Comput. Mech., 10, 307-318 (1992) · Zbl 0764.65068
[2] Touzot, G.; Villon, P.; Nayroles, B., La méthode des éléments diffus, C. R. Acad. Sci. Paris Sér. II, 313, 133-138 (1991) · Zbl 0725.73085
[3] Ciarlet, P. G., The Finite Elements Method for Elliptic Problems (1978), North-Holland: North-Holland Amsterdam · Zbl 0445.73043
[4] Han, W.; Meng, X., Error analysis of the reproducing kernel particle method, Comput. Meth. Appl. Mech. Engrg., 190, 6157-6181 (2001) · Zbl 0992.65119
[5] Lancaster, P.; Salkauskas, K., Curve and Surface Fitting. An Introduction (1986), Academic Press: Academic Press San Diego · Zbl 0649.65012
[7] Shepard, D. D., A two dimensional interpolation function for irregularly spaced data, (Proc. 23rd Nat. Conf. ACM (1968), ACM Press: ACM Press NY)
[8] Lu, Y. Y.; Belyschko, T.; Gu, L., Element-free Galerkin methods, Internat. J. Numer. Meth. Engrg., 37, 229-256 (1994) · Zbl 0796.73077
[11] Teng, S. H.; Li, X. Y.; Üngör, A., Advancing front meets sphere packing, Internat. J. Numer. Methods Engrg., 49, 1 & 2, 61-81 (2000) · Zbl 0966.65096
[12] Teng, S. H.; Li, X. Y.; Üngör, A., Generating a good quality point set for the meshless methods, CMES, 1, 1, 10-17 (2000)
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