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Un schéma d'interpolation rationnel sur un quadrilatère de classeC2

Published online by Cambridge University Press:  15 April 2002

Mohammed Laghchim-Lahlou*
Université Cadi Ayyad, Faculté des Sciences Semlalia, Département de Mathématiques, BP S15, 40000 Marrakech, Maroc. (
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Let $\mathcal{Q}$ be a partition of a polygonal domain of the plan into convexe quadrilaterals. Given a regular function f , we construct a function πƒ ∈ C2(Ω), interpolating position values and derivatives of f up of order 2 at vertices of $\mathcal{Q}.$ On each quadrilateral $Q\in\mathcal{Q},$ πƒ|Q is a finite element obtained from a polynomial scheme of FVS type by adding some rational functions.

Research Article
© EDP Sciences, SMAI, 2000

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K.N. Agbeve, Eléments finis triangulaires rationnels de classe C k . Thèse de Doctorat, Université de Nantes (1993).
Alfeld, P., A bivariate C 2 Clough-Tocher scheme. Comput. Aided Geom. Design 1 (1984) 257-267. CrossRef
Argyris, J.H., Fried, I. et Scharpf, D.W., The TUBA family of plate elements for the matrix displacement method. The Aeronautical Journal of the Royal Aeronautical Society 72 (1968) 701-709.
Farin, G., Triangular Bernstein-Bézier patches. Comput. Aided Geom. Design 2 (1986) 83-127. CrossRef
G. Fraeijs de Veubeke, Bending and Stretching of plates, in Conference on matrix methods in structural mechanics, Wright Patterson A.F.B., Ohio (1965).
Herron, G., A characterisation of C 1 discrete triangular interpolants. SIAM J. Numer. Anal . 22 (1985) 811-819. CrossRef
Lai, M.J., On dual functionals of polynomials in B-form. J. Approx. Theory 67 (1991) 19-37. CrossRef
Laghchim-Lahlou, M. et Sablonnière, P., Triangular finite elements of HCT type and class Cp . Adv. Comput. Math. 2 (1994) 101-122. CrossRef
Laghchim-Lahlou, M. et Sablonnière, P., C r -finite elements of Powell-Sabin type on the three direction mesh. Adv. Comput. Math. 6 (1996) 191-206. CrossRef
A. Le Méhauté, Interpolation et approximation par des fonctions polynômiales par morceaux dans $\mathbb{R}^{n}$ . Thèse de Doctorat ès Sciences, Université de Rennes (1984).
Laghchim-Lahlou, M. et Sablonnière, P., Quadrilateral finite elements of FVS type and class Cp . Numer. Math . 70 (1995) 229-243. CrossRef
Lai, M.J. et Schumaker, L.L., Scattered data interpolation using C 2 Supersplines of degree six. SIAM J. Numer. Anal . 34 (1997) 905-921. CrossRef
Schumaker, L.L., 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.
Wang, T., A C 2 quintic spline interpolation scheme on triangulation. Comput. Aided Geom. Design 9 (1992) 379-386. CrossRef
A. Ženišek, A general theorem on triangular finite C m -elements. RAIRO Anal. Numér . 8 (1974) 119-127.
O.C. Zienkiewicz, The finite element method in structural continum mechanics. Mc Graw Hill, London (1967).