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Convergence of dual finite element approximations for unilateral boundary value problems. (English) Zbl 0462.65064


MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
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References:

[1] I. Hlaváček: Dual finite element analysis for unilateral boundary value problems. Apl. mat. 22 (1977), 14-51.
[2] I. Hlaváček: Dual finite element analysis for elliptic problems with obstacles on the boundary I. Apl. mat. 22 (1977), 244-255.
[3] I. Hlaváček: Dual finite element analysis for semi-coercive unilateral boundary value problems. Apl. mat. 23 (1978), 52-71.
[4] J. Haslinger, and I. Hlaváček: Convergence of a finite element method based on the dual variaional formulation. Apl. mat. 21 (1976), 43 - 65.
[5] J. Céa: Optimisation, théorie et algorithmes. Dunod, Paris 1971. · Zbl 0211.17402
[6] I. Hlaváček, J. Lovíšek: A finite element analysis for the Signorini problem in plane elastostatics. Apl. mat. 22 (1.977), 215 - 228. · Zbl 0369.65031
[7] G. Fichera: Boundary value problems of elasticity with unilateral constraints. Encycl. of Physics (ed. by S. Fliigge), vol. VIa/2, Springer- Verlag, Berlin, 1972.
[8] J. Frehse: Regularity of solutions for problems with thin obstacles. Math. Zeitschrift 143 (1975), 279-288. · Zbl 0295.49003
[9] P. Grisvard, G. Iooss: Problèmes aux limites unilatéraux dans les domaines non réguliers. Publ. Seminaires Math., Univ. de Rennes, 1976.
[10] I. Hlaváček: Convergence of an equilibrium finite element model for plane elastostatics. Apl. mat. 24 (1979), 427-457.
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