Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Interpolation error estimates for the reduced Hsieh-Clough-Tocher triangle
HTML articles powered by AMS MathViewer

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.
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC: 65N30, 41A25
  • Retrieve articles in all journals with MSC: 65N30, 41A25
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