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Ciarlet, Philippe G.

Interpolation error estimates for the reduced Hsieh-Clough-Tocher triangle. (English) Zbl 0378.65010

Math. Comput. 32, 335-344 (1978).
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Cited in 15 Documents

MSC:

65D05 Numerical interpolation
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
41A25 Rate of convergence, degree of approximation
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\textit{P. G. Ciarlet}, Math. Comput. 32, 335--344 (1978; Zbl 0378.65010)
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References:

[1] James H. Bramble and Miloš Zlámal, Triangular elements in the finite element method, Math. Comp. 24 (1970), 809 – 820. · Zbl 0226.65073
[2] P. G. Ciarlet, Sur l’élément de Clough et Tocher, Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge 8 (1974), no. R-2, 19 – 27 (French, with loose English summary). · Zbl 0306.65070
[3] Philippe G. Ciarlet, Numerical analysis of the finite element method, Les Presses de l’Université de Montréal, Montreal, Que., 1976. Séminaire de Mathématiques Supérieures, No. 59 (Été 1975). · Zbl 0353.73067
[4] Philippe G. Ciarlet, The finite element method for elliptic problems, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1978. Studies in Mathematics and its Applications, Vol. 4. · Zbl 0383.65058
[5] P. G. Ciarlet and P.-A. Raviart, General Lagrange and Hermite interpolation in \?\(^{n}\) with applications to finite element methods, Arch. Rational Mech. Anal. 46 (1972), 177 – 199. · Zbl 0243.41004
[6] R. W. CLOUGH & J. L. TOCHER, ”Finite element stiffness matrices for analysis of plates in bending,” in Proc. Conf. on Matrix Methods in Structural Mechanics, Wright-Patterson A.F.B., Ohio, 1965.
[7] J. NEČAS, Les Méthodes Directes en Théorie des Equations Elliptiques, Masson, Paris, 1967. · Zbl 1225.35003
[8] Peter Percell, On cubic and quartic Clough-Tocher finite elements, SIAM J. Numer. Anal. 13 (1976), no. 1, 100 – 103. · Zbl 0319.65064
[9] P.-A. RAVIART, Méthode des Eléments Finis, Lecture Notes (D.E.A. Analyse Numérique), Laboratoire d’Analyse Numérique, Université Pierre et Marie Curie (Paris VI), 1972.
[10] Alexander Ženíšek, Interpolation polynomials on the triangle, Numer. Math. 15 (1970), 283 – 296. · Zbl 0216.38901
[11] A. ŽENÍŠEK, ”A general theorem on triangular finite \( {C^{(m)}}\)-elements,” Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge Anal. Numér. R-2, 1974, pp. 119-127.
[12] O. C. Zienkiewicz, The finite element method in engineering science, McGraw-Hill, London-New York-Düsseldorf, 1971. The second, expanded and revised, edition of The finite element method in structural and continuum mechanics. · Zbl 0237.73071
[13] M. ZLÁMAL, ”On the finite element method,” Numer. Math., v. 12, 1968, pp. 394-409. · Zbl 0176.16001
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