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Birkhoff, Garrett; Mansfield, Lois

Compatible triangular finite-elements. (English) Zbl 0284.35021

J. Math. Anal. Appl. 47, 531-553 (1974).
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Cited in 14 Documents

MSC:

35J30 Higher-order elliptic equations
35A99 General topics in partial differential equations
35A35 Theoretical approximation in context of PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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References:

[1] (Aziz, A. K., Symposium on Mathematical Foundations of the Finite Element Method (1973), Academic Press)
[2] Barnhill, R. E.; Birkhoff, G.; Gordon, W. J., J. Approx. Theory, 8, 114-128 (1973), Revised version in · Zbl 0271.41002
[3] Mansfield, Lois, Error bounds for smooth interpolation in triangles, J. Approx. Theory, 11 (1974), in press · Zbl 0286.41001
[4] Bazeley, G. P.; Cheung, Y. K.; Irons, B. M.; Zienkiewicz, O. C., Triangular elements in bending …, (Proc. Conf. Matrix Methods in Struct. Mech. (1965), Air Force Inst. of Tech: Air Force Inst. of Tech Wright Patterson A. F. Base, Ohio)
[5] Birkhoff, G., Tricubic interpolation in triangles, (Proc. Nat. Acad. Sci., 68 (1971)), 1162-1164 · Zbl 0242.41007
[6] Birkhoff, G., Interpolation to boundary data in triangles, J. Math. Anal. Appl., 42, 474-484 (1973) · Zbl 0262.41003
[7] Bramble, J. H.; Zlámal, M., Triangular elements in the finite element method, Math. Comp., 24, 809-820 (1970) · Zbl 0226.65073
[8] Felippa, C. A.; Clough, R. W., The finite element in solid mechanics, (SIAM—AMS Proceedings, Vol. II (1970), Amer. Math. Soc: Amer. Math. Soc Providence, RI), 210-252 · Zbl 0222.73107
[9] Goël, J. J., Construction of basic functions for … Ritz’ method, Numer. Math., 12, 435-447 (1968) · Zbl 0271.65061
[10] Irons, B. M., A conforming quartic triangular element for plate bending, Int. J. Numer. Meth. Eng., 1, 29-45 (1969) · Zbl 0247.73071
[11] Mitchell, A. R., Introduction to the mathematics of finite elements, (Whiteman, J. R., The Mathematics of Finite Elements with Applications (1972), Academic Press: Academic Press London) · Zbl 0288.65061
[12] Ženišek, M., Interpolation polynomials on the triangle, Numer. Math., 15, 283-296 (1970) · Zbl 0216.38901
[13] Zienkiewicz, O. C., The Finite Element Method (1971), McGraw-Hill: McGraw-Hill New York · Zbl 0237.73071
[14] Dupuis, G.; Goël, J.-J, Finite element with high degree of regularity, Int. J. Numer. Meth. Eng., 2, 563-577 (1970) · Zbl 0257.65089
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