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Compatible triangular finite-elements. (English) Zbl 0284.35021


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
Full Text: DOI

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
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[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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