Un schéma d’interpolation rationnel sur un quadrilatère de classe C 2
Laghchim-Lahlou, Mohammed
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 34 (2000), p. 913-922 / Harvested from Numdam
Publié le : 2000-01-01
@article{M2AN_2000__34_5_913_0,
     author = {Laghchim-Lahlou, Mohammed},
     title = {Un sch\'ema d'interpolation rationnel sur un quadrilat\`ere de classe $C^2$},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {34},
     year = {2000},
     pages = {913-922},
     mrnumber = {1837760},
     zbl = {0974.65013},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/M2AN_2000__34_5_913_0}
}
Laghchim-Lahlou, Mohammed. Un schéma d’interpolation rationnel sur un quadrilatère de classe $C^2$. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 34 (2000) pp. 913-922. http://gdmltest.u-ga.fr/item/M2AN_2000__34_5_913_0/

[1] K.N. Agbeve, Eléments finis triangulaires rationnels de classe Ck. Thèse de Doctorat, Université de Nantes (1993).

[2] P. Alfeld, A bivariate C2 Clough-Tocher scheme. Comput. Aided Geom. Design 1 (1984) 257-267. | Zbl 0597.65005

[3] J.H. Argyris, I. Fried et D.W. Scharpf, The TUBA family of plate elements for the matrix displacement method. The Aeronautical Journal of the Royal Aeronautical Society 72 (1968) 701-709.

[4] G. Farin, Triangular Bernstein-Bézier patches. Comput. Aided Geom. Design 2 (1986) 83-127. | MR 867116

[5] G. Fraeijs De Veubeke, Bending and Stretching of plates, in Conference on matrix methods in structural mechanics, Wright Patterson A.F.B., Ohio (1965).

[6] G. Herron, A characterisation of C1 discrete triangular interpolants. SIAM. J. Numer. Anal. 22 (1985) 811-819. | MR 795955 | Zbl 0593.65008

[7] M.J. Lai, On dual functionals of polynomials in B-form. J. Approx. Theory 67 (1991) 19-37. | MR 1127818 | Zbl 0738.41014

[8] M. Laghchim-Lahlou et P. Sablonnière, Triangular finite elements of HCT type and class Cp. Adv. Comput. Math. 2 (1994) 101-122. | MR 1266026 | Zbl 0832.65003

[9] M. Laghchim-Lahlou et P. Sablonnière, Cr-finite elements of Powell-Sabin type on the three direction mesh. Adv. Comput. Math. 6 (1996) 191-206. | MR 1431792 | Zbl 0867.65002

[10] A. Le Méhauté, Interpolation et approximation par des fonctions polynômiales par morceaux dans ℝn. Thèse de Doctorat ès Sciences, Université de Rennes (1984).

[11] M. Laghchim-Lahlou et P. Sablonnière, Quadrilateral finite elements of FVS type and class Cp. Numer. Math. 70 (1995)229-243. | MR 1324738 | Zbl 0824.41012

[12] M.J. Lai et L.L. Schumaker, Scattered data interpolation using C2 Supersplines of degree six. SIAM. J. Numer. Anal. 34 (1997) 905-921. | MR 1451106 | Zbl 0872.41004

[13] L.L. Schumaker, On the dimension of spaces of piecewise polynomials in two variables, in Multivariate Approximation Theory, W. Schempp et K. Zeller Eds., Birkhäuser Verlag, ISNM 51 (1979) 396-412. | MR 560683 | Zbl 0461.41006

[14] T. Wang, A C2 quintic spline interpolation scheme on triangulation. Comput. Aided Geom. Design 9 (1992) 379-386. | MR 1192667 | Zbl 0770.65005

[15] A. Ženišek, A general theorem on triangular finite Cm-elements. RAIRO Anal. Numér. 8 (1974) 119-127. | Numdam | MR 388731 | Zbl 0321.41003

[16] O.C. Zienkiewicz, The finite element method in structural continum mechanics. Mc Graw Hill, London (1967). | Zbl 0237.73071