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Article

Keywords:
unilateral plate problem; inner obstacle; mixed finite elements; Herrmann-Johnson mixed model; fourth order variational inequality
Summary:
A unilateral problem of an elastic plate above a rigid interior obstacle is solved on the basis of a mixed variational inequality formulation. Using the saddle point theory and the Herrmann-Johnson scheme for a simultaneous computation of deflections and moments, an iterative procedure is proposed, each step of which consists in a linear plate problem. The existence, uniqueness and some convergence analysis is presented.
References:
[1] Brezzi, F.: On the existence, uniqueness and approximations of saddle-point problems arising from Lagrange multipliers. vol. 8-R2, R. A. I. R. O., 1974, pp. 129–151. MR 0365287
[2] Brezzi, F.–Raviart, P. A.: Mixed finite element methods for 4th order elliptic equations. Topics in Numer. Anal., vol. III (ed. by J. J. H. Miller), Academic Press, London, 1977, pp. 33–56. MR 0657975 | Zbl 0434.65085
[3] Ekeland, I.–Temam, R.: Analyse convexe et problèmes variationnels. Dunod, Paris, 1974. Zbl 0281.49001
[4] Glowinski, R.–Lions, J. L.–Trémolières, R.: Numerical analysis of variational inequalities. North-Holland, Amsterdam, 1981. MR 0635927 | Zbl 0463.65046
[5] Haslinger, J.: Mixed formulation of variational inequalities and its approximation. Apl. Mat. 26 (1981), 462–475. MR 0634283
[6] Nečas, J.: Les méthodes directes en théorie des équations elliptiques. Academia, Prague, 1967. MR 0227584
[7] Comodi, M. I.: Approximation of a bending plate problem with a boundary unilateral constraint. Numer. Math. 47 (1985), 435–458. DOI 10.1007/BF01389591 | MR 0808562 | Zbl 0581.73022
[8] Ciarlet, P.G.: The finite element method for elliptic problems. North-Holland, Amsterdam, 1978. MR 0520174 | Zbl 0383.65058
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