Geodesic
On numerical solution of a variational inequality of the 4th order by finite element method
Applications of Mathematics, Tome 23 (1978) no. 5, pp. 334-345 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The problem of a thin elastic plate, deflection of which is limited below by a rigid obstacle is solved. Using Ahlin's and Ari-Adini's elements on rectangles, the convergence is established and SOR method with constraints is proposed for numerical solution.
The problem of a thin elastic plate, deflection of which is limited below by a rigid obstacle is solved. Using Ahlin's and Ari-Adini's elements on rectangles, the convergence is established and SOR method with constraints is proposed for numerical solution.
DOI : 10.21136/AM.1978.103760
Classification : 31A30, 35J20, 49A29, 65K05, 65N30, 73K10, 74K20, 74S05, 74S30, 90C20
Keywords: quadratic programming; elastic clamped plate; algorithm; energy functional; convergence; minimization problem; numerical solution; finite element method 
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Haslinger, Jaroslav. On numerical solution of a variational inequality of the 4th order by finite element method. Applications of Mathematics, Tome 23 (1978) no. 5, pp. 334-345. doi: 10.21136/AM.1978.103760

[1] Cea J.: Optimisation théorie et algorithmes. Dunod, Paris 1971. | MR | Zbl

[2] Ciarlet P. G.: Conforming and nonconforming finite element methods for solving the plate problem. Conference on the numerical solution of differential equations, University of Dundee, July 1973, 03-06. | MR

[3] Ciarlet P. G., Raviart P. A.: General Lagrange and Hermite interpolation in $R_n$ with applications to finite element methods. Arch. Rat. Anal. Vol. 46 (1972), 177- 199. | DOI | MR | Zbl

[4] Glowinski R.: Analyse numerique d'inequations variationnelles d'ordre 4. (preprint of University Paris VI).

[5] Jakovlev G. N.: The boundary properties of the functions belonging to the class $W^{1,p} on domains with conical or angular points. Trans. Moscow Math. Soc. (1967), 227--313.

[6] Janovský V., Procházka P.: The nonconforming finite element method in the problem of clamped plate with ribs. Apl. Mat. 21 (1976), No 4, 273 - 289. | MR

[7] Glowinski R., Lions J. L., Trémolieres R.: Analyse numérique des inéquations variationnelles. Dunod, Paris 1976.

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