Error estimates for Modified Local Shepard's Formulas in Sobolev spaces
ESAIM: Mathematical Modelling and Numerical Analysis (2010)
- Volume: 37, Issue: 6, page 973-989
- ISSN: 0764-583X
Access Full Article
topAbstract
topHow to cite
topReferences
top- R.A. Adams, Sobolev Spaces. Academic Press, Inc., Orlando (1975).
- S.C. Brener and L.R. Scott, The Mathematical Theory of Finite Elements Methods. Springer-Verlag, New York (1994).
- P.G. Ciarlet, The Finite Elements Method for Elliptic Problems. North-Holland, Amsterdam (1978).
- C.A. Duarte and J.T. Oden, Hp clouds-a meshless method to solve boundary-value problems. Technical Report 95-05, TICAM, The University of Texas at Austin (1995).
- C.A. Duarte and J.T. Oden, H-p clouds-an h-p meshless method. Numer. Methods Partial Differential Equations1 (1996) 1–34.
- C.A.M. Duarte, T.J. Liszka and W.W. Tworzydlo, hp-meshless cloud method. Comput. Methods Appl. Mech. Engrg.139 (1996) 263–288.
- R.G. Durán, On polynomial approximation in Sobolev spaces. SIAM J. Numer. Anal.20 (1983) 985–988.
- W. Han and X. Meng, Error analysis of the reproducing kernel particle method. Comput. Methods Appl. Mech. Engrg.190 (2001) 6157–6181.
- Y.Y. Lu, T. Belyschko and L. Gu, Element-free Galerkin methods. Internat. J. Numer. Methods Engrg.37 (1994) 229–256.
- E. Oñate, R. Taylor, O.C. Zienkiewicz and S. Idelshon, Moving least square approximations for the solutions of differential equations. Technical Report, CIMNE, Santa Fé, Argentina (1995).
- R.J. Renka, Multivariate interpolation of large sets of scattered data. ACM Trans. Math. Software14 (1988) 139–148.
- L.L. Schumaker, Fitting surfaces to scattered data, in Approximation Theory II, Academic Press, Inc., New York (1970).
- D.D. Shepard, A Two Dimensional Interpolation Function for Irregularly Spaced Data. Proc. 23rd Nat. Conf. ACM (1968).
- R. Verfúrth, A note on polynomial approximation in Sobolev spaces. ESAIM: M2AN33 (1999) 715–719.
- C. Zuppa, Error estimates for modified local Shepard's formulaes. Appl. Numer. Math. (to appear).
- C. Zuppa, Good quality point sets and error estimates for moving least square approximations. Appl. Numer. Math.47 (2003) 575–585.