General lagrange and hermite interpolation in Rn with applications to finite element methods

Aubin, J.P., Behavior of the approximate solution of boundary value problems for linear elliptic operators by Galerkin's and finite difference methods. Ann. Scuola Norm. Sup. Pisa 21, 559–639 (1967).

Aubin, J.P., Approximation des espaces de distributions et des opérateurs différentiels. Bull. Soc. Math. France (1967), Mémoire No 12.

Babuška, Ivo, The finite element method for elliptic differential equations (Symp. on the Numerical Solution of Partial Differential Equations, Univ. of Maryland, 1970). Numerical Solution of Partial Differential Equations-II (B. Hubbard, ed.), p. 69–106. New York: Academic Press 1971.

Babuška, Ivo, Error bounds for finite element method. Numer. Math. 16, 322–333 (1971).

Bell, K., A refined triangular plate bending finite element. Int. J. Numer. Math. Engineering 1, 101–121 (1969).

Birkhoff, G., M. Schultz, & R.S. Varga, Piecewise Hermite interpolation in one and two variables with applications to partial differential equations. Numer. Math. 11, 232–256 (1968).

Bramble, James H., Variational Methods for the Numerical Solution of Elliptic Problems (Lecture notes). Chalmers Institute of Technology and the University of Göteborg, Sweden, 1970.

Bramble, J.H., & S.R. Hilbert, Estimation of linear functionals on Sobolev spaces with applications to Fourier transforms and spline interpolation. SIAM J. Numer. Anal. 7, 112–124 (1970).

Bramble, J.H., & S.R. Hilbert, Bounds for a class of linear functionals with applications to Hermite interpolation. Numer. Math. 16, 362–369 (1971).

Bramble, James H., & Miloš Zlámal, Triangular elements in the finite element method. Math. Comp. 24, 809–820 (1970).

Cartan, Henri, Calcul Differentiel. Paris: Hermann 1967.

Ciarlet, P.G., Some results in the theory of nonnegative matrices. Linear Algebra and Appl. 1, 139–152 (1968).

Ciarlet, P.G., & C. Wagschal, Multipoint Taylor formulas and applications to the finite element method. Numer. Math. 17, 84–100 (1971).

Coatmélec, Christian, Approximation et interpolation des fonctions différentiables de plusieurs variables. Ann. Sci. Ecole Norm. Sup. (3) 83, 271–341 (1966).

Dieudonnè, J., Foundations of Modern Analysis. New York: Academic Press Inc. 1960.

Fix, G., & G. Strang, Fourier analysis of the finite element method in Ritz-Galerkin theory. Studies in Appl. Math. 48, 265–273 (1969).

Frederickson, Paul O., Triangular spline interpolation. Math. Report No. 6, Lakehead Univ. 1970.

Guenther, R.B., & E. L. Roetman, Some observations on interpolation in higher dimensions. Math. Comp. 24, 517–522 (1970).

Guglielmo, F. di, Méthode des éléments finis: Une famille d'approximation des espaces de Sobolev par les translatées de p fonctions. Calcolo 7, 185–234 (1970).

Hall, C.A., Bicubic interpolation over triangles. J. Math. Mech. 19, 1–11 (1969).

Nečas, Jindřich, Les Méthodes Directes en Théorie des Equations Elliptiques. Paris: Masson 1967.

Nicolaides, R.A., On Lagrange interpolation in n variables. Institute of Computer Sciences (London), Tech. Note ICSI 274, 1970.

Nicolaides, R.A., On a class of finite elements generated by Lagrange interpolation II. Institute of Computer Science (London), Techn. Note ICSI 329, 1971.

Nicolaides, R.A., On a class of finite elements generated by Lagrange interpolation. To appear.

Nitsche, J., Interpolation in Sobolevschen Funktionenräumen. Numer. Math. 13, 334–343 (1969).

Nitsche, J., Lineare Spline-Funktionen und die Methode von Ritz für elliptische Randwertprobleme. Arch. Rational Mech. Anal. 36, 348–355 (1970).

Salzer, Herbert E., Formulas for bivariate hyperosculatory interpolation. Math. Comp. 25, 119–133 (1971).

Schultz, M. H., L2-multivariate approximation theory. SIAM J. Numer. Anal. 6, 184–209 (1969).

Strang, Gilbert, The finite element method and approximation theory (Symp. on the Numerical Solution of Partial Differential Equations, Univ. of Maryland, 1970). Numerical Solution of Partial Differential Equations-II (B. Hubbard, ed.), p. 547–583. New York: Academic Press 1971.

Strang, Gilbert, & George Fix, Chapter III of: An Analysis of the Finite Element Method. To appear.

Taylor, Angus E., Introduction to Functional Analysis. New-York: John Wiley 1958.

Thacher, Jr., Henry C., Derivation of interpolation formulas in several independent variables. Ann. New York Acad. Sci. 86, 758–775 (1960).

Thacher, Jr., Henry C., & W.E. Milne, Interpolation in several variables. J. Soc. Indust. Appl. Math. 8, 33–42 (1960).

Ženíšek, Alexander, Interpolation polynomials on the triangle. Numer. Math. 15, 283–296 (1970).

Zlámal, Miloš, On the finite element method. Numer. Math. 12, 394–409 (1968).

Zlámal, Miloš, A finite element procedure of the second order of accuracy. Numer. Math. 14, 394–402 (1970).