Interpolation error estimates for the reduced Hsieh-Clough-Tocher triangle
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- by Philippe G. Ciarlet PDF
- Math. Comp. 32 (1978), 335-344 Request permission
Abstract:
We study the unisolvence and interpolation properties of the reduced Hsieh-Clough-Tocher triangle. This finite element of class ${\mathcal {C}^1}$, which has only nine degrees of freedom, can be used in the numerical approximation of plate problems.References
- James H. Bramble and Miloš Zlámal, Triangular elements in the finite element method, Math. Comp. 24 (1970), 809–820. MR 282540, DOI 10.1090/S0025-5718-1970-0282540-0
- 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 English summary). MR 381349
- Philippe G. Ciarlet, Numerical analysis of the finite element method, Séminaire de Mathématiques Supérieures, No. 59 (Été 1975), Les Presses de l’Université de Montréal, Montreal, Que., 1976. MR 0495010
- Philippe G. Ciarlet, The finite element method for elliptic problems, Studies in Mathematics and its Applications, Vol. 4, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1978. MR 0520174
- P. G. Ciarlet and P.-A. Raviart, General Lagrange and Hermite interpolation in $\textbf {R}^{n}$ with applications to finite element methods, Arch. Rational Mech. Anal. 46 (1972), 177–199. MR 336957, DOI 10.1007/BF00252458 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. J. NEČAS, Les Méthodes Directes en Théorie des Equations Elliptiques, Masson, Paris, 1967.
- Peter Percell, On cubic and quartic Clough-Tocher finite elements, SIAM J. Numer. Anal. 13 (1976), no. 1, 100–103. MR 408198, DOI 10.1137/0713011 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.
- Alexander Ženíšek, Interpolation polynomials on the triangle, Numer. Math. 15 (1970), 283–296. MR 275014, DOI 10.1007/BF02165119 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.
- 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. MR 0315970 M. ZLÁMAL, "On the finite element method," Numer. Math., v. 12, 1968, pp. 394-409.
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Math. Comp. 32 (1978), 335-344
- MSC: Primary 65N30; Secondary 41A25
- DOI: https://doi.org/10.1090/S0025-5718-1978-0482249-1
- MathSciNet review: 482249