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Mansfield, Lois

A Clough-Tocher type element useful for fourth order problems over nonpolygonal domains. (English) Zbl 0382.65060

Math. Comput. 32, 135-142 (1978).
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Cited in 6 Documents

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J40 Boundary value problems for higher-order elliptic equations
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\textit{L. Mansfield}, Math. Comput. 32, 135--142 (1978; Zbl 0382.65060)
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References:

[1] Garrett Birkhoff, Tricubic polynomial interpolation, Proc. Nat. Acad. Sci. U.S.A. 68 (1971), 1162 – 1164. · Zbl 0242.41007
[2] Garrett Birkhoff and Lois Mansfield, Compatible triangular finite elements, J. Math. Anal. Appl. 47 (1974), 531 – 553. · Zbl 0284.35021
[3] 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 loose English summary). · Zbl 0306.65070
[4] Philippe G. Ciarlet, Numerical analysis of the finite element method, Les Presses de l’Université de Montréal, Montreal, Que., 1976. Séminaire de Mathématiques Supérieures, No. 59 (Été 1975). · Zbl 0353.73067
[5] R. W. CLOUGH & J. L. TOCHER, ”Finite element stiffness matrices for analysis of plates in bending,” Conferences on Matrix Methods in Structural Mechanics, Wright-Patterson A. F. B., Ohio, 1965.
[6] Lois Mansfield, Approximation of the boundary in the finite element solution of fourth order problems, SIAM J. Numer. Anal. 15 (1978), no. 3, 568 – 579. · Zbl 0391.65047
[7] Miloš Zlámal, Curved elements in the finite element method. I, SIAM J. Numer. Anal. 10 (1973), 229 – 240. · Zbl 0285.65067
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