Multipoint Taylor formulas and applications to the finite element method. (English) Zbl 0199.50104

Full Text: DOI EuDML


[1] Cartan, Henri: Calcul Différentiel. Paris: Hermann 1967.
[2] Ciarlet, P. G., Schultz, M. H., Varga, R. S.: Numerical methods of high order accuracy for nonlinear boundary value problems. V. Monotone operator theory. Numer. Math.13, 51-77 (1969). · Zbl 0181.18603
[3] Coatmélec, Christian: Approximation et interpolation des fonctions différentiables de plusieurs variables. Ann. Sci. Ecole Norm. Sup. (3)83, 271-341 (1966).
[4] Courant, R.: Variational methods for the solution of problems of equilibrium and vibrations. Bull. Amer. Math. Soc.49, 1-23 (1943). · Zbl 0063.00985
[5] Dieudonné, J.: Foundations of modern analysis. New York: Academic Press Inc. 1960. · Zbl 0100.04201
[6] Di Guglielmo, Francis: Construction d’approximations des espaces de SobolevH m (R n ),m entier positif, sur des réseaux en simplexes. C. R. Acad. Sc. Paris268, 314-317 (1969). · Zbl 0167.14701
[7] Fraeijs de Veubeke, B.: Displacement and equilibrium models in the finite element method. Stress analysis, chapter 9 (O. C. Zienkiewicz and G. S. Holister editors). London: J. Wiley 1965.
[8] Friedrichs, K. O., Keller, H. B.: A finite difference scheme for generalized Neumann problems. Numerical solution of partial differential equations (Proceedings of a Symposium held at the University of Maryland, May 3-8, 1965, J. H. Bramble, editor), pp. 1-19. New York: Academic Press 1966.
[9] Oganesjan, L. A.: Convergence of difference schemes in case of improved approximation of the boundary. ?. Vy?isl. Mat. i Mat. Fiz.6, 1029-1042 (1966)
[10] Tong, Pin, Pian, T. H. H.: The convergence of finite element method in solving linear elastic problems. Int. J. Solids Structures3, 865-879 (1967). · Zbl 0149.42802
[11] Wallace, Andrew H.: An introduction to algebraic topology. Oxford: Pergamon Press 1957. · Zbl 0080.37903
[12] Zienkiewicz, O. C.: The finite element method in structural and continuum mechanics. London: McGraw-Hill Publishing Co. Ltd. 1967. · Zbl 0189.24902
[13] Zlámal, Milo?.: On the finite element method. Numer. Math.12, 394-409 (1968). · Zbl 0176.16001
[14] ?: On some finite element procedures for solving second order boundary value problems. Numer. Math.14, 42-48 (1969). · Zbl 0215.55704
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.