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Convergence of a penalty-finite element approximation for an obstacle problem. (English) Zbl 0469.65044


MSC:

65K10 Numerical optimization and variational techniques
74S05 Finite element methods applied to problems in solid mechanics
49M30 Other numerical methods in calculus of variations (MSC2010)
74K15 Membranes
49J40 Variational inequalities

Citations:

Zbl 0427.65077
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References:

[1] Aubin, J.P.: Estimate of the error in the approximation of optimization problems with constraints by problems without constraints. In: Control theory and the calculus of variation, (A.V. Balakrishnan, ed.), pp. 153-173 New York: Academic Press, 1979
[2] Babu?ka, I.: The finite element method with lagrange multipliers. Numer. Math.20, 179-192 (1973) · Zbl 0258.65108 · doi:10.1007/BF01436561
[3] Bercovier, M.: Perturbation of mixed variational problems. Application to mixed finite element method. RAIRO, Numerical Analysis12, 211-236 (1978) · Zbl 0428.65059
[4] Brezis, H., Stampacchia, G.: Sur la regularite de la solution d’inequations elliptiques. Bull. Soc. Math. France96: 153-180 (1968)
[5] Brezzi, F.: On the existence, uniqueness and approximations of saddle-point problems arising from lagrangian multipliers. RAIRO, R.2, 129-151 (1974) · Zbl 0338.90047
[6] Brezzi, F., Hager, W.W., Raviart, P.A.: Error estimates for the finite element solution of variational inequalities?Part I: Primal theory. Numer. Math.28, 431-443 (1977) · Zbl 0369.65030 · doi:10.1007/BF01404345
[7] Brezzi, F., Hager, W.W., Raviart, P.A.: Error estimates for the finite element solution of variational inequalities?Part II: Mixed methods. Numer. Math.31, 1-16 (1978) · Zbl 0427.65077 · doi:10.1007/BF01396010
[8] Glowinski, R., Lions, J.L., Trémolièces, R.: Analyse numérique des inéquations variationelles. Paris: Dunod, 1976
[9] Falk, R.S.: Error estimates for the approximation of a class of variational inequalities. Math. Comput.28, 963-971 (1974) · Zbl 0297.65061 · doi:10.1090/S0025-5718-1974-0391502-8
[10] Falk, R.S.: Approximation of an elliptic boundary value problem with unilateral constraints. Rev. Française Automat. Informat. Recherche Opérationnelle R2, 5-12 (1975) · Zbl 0316.65024
[11] Kikuchi, N.: Convergence of a penalty method for variational inequalities. TICOM Report 79-16. The University of Texas at Austin, 1979 · Zbl 0441.65087
[12] Lions, J.-L.: Quelques methodes de résolution des problèmes aux limites non linéaires. Paris: Dunod, 1969
[13] Lions, J.-L.: Sur quelques questions d’analyse, de mécanique et de contrôle optimal. Montreal: Les Presses de l’Universite, 1976 · Zbl 0339.49003
[14] Mosco, U., Strang, G.: One-sided, approximation and variational inequalities. Bull. Amer. Math. Soc.,80, 308-312 (1974) · Zbl 0278.35026 · doi:10.1090/S0002-9904-1974-13477-4
[15] Oden, J.T., Kikuchi, N., Song, Y.J.: An analysis of exterior penalty methods and reduced integration for finite element approximations of contact problems in incompressible elasticity. TICOM Report 80-2, The University of Texas at Austin, 1980
[16] Temam, R.: Navier-Stokes equations. Amsterdam: North-Holland, 1977 · Zbl 0383.35057
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