On numerical solution of a variational inequality of the 4th order by finite element method. (English) Zbl 0399.65084

Haslinger, Jaroslav

Apl. Mat. 23, 334-345 (1978).

MSC:

65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J20	Variational methods for second-order elliptic equations
65K05	Numerical mathematical programming methods
90C20	Quadratic programming
74K20	Plates
74S05	Finite element methods applied to problems in solid mechanics
74S30	Other numerical methods in solid mechanics (MSC2010)
31A30	Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions

Keywords:

Quadratic Programming; Elastic Clamped Plate; Algorithm; Energy Functional; Convergence; Minimization Problem; Numerical Solution; Finite Element Method

References:

[1]	Cea J.: Optimisation théorie et algorithmes. Dunod, Paris 1971. · Zbl 0211.17402
[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.
[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. · Zbl 0243.41004
[4]	Glowinski R.: Analyse numerique d’inequations variationnelles d’ordre 4.
[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.
[7]	Glowinski R., Lions J. L., Trémolieres R.: Analyse numérique des inéquations variationnelles. Dunod, Paris 1976. · Zbl 0358.65091