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

### 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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### 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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