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Article

Keywords:
dual variational formulation; free boundary value problem; finite element method; elliptic inequality; rate of convergence; Ritz approximations
Summary:
The dual variational formulation of some free boundary value problem is given and its approximation by finite element method is studied, using piecewise linear elements with non-positive divergence.
References:
[1] I. Babuška: Approximation by hill-functions II. Institute for fluid Dynamics and Applied mathematics. Technical note BN-708. MR 0305550
[2] F. Brezzi W. W. Hager P. A. Raviart: Error estimates for the finite element solution of variational inequalities. Part I: Primal Theory. (preprint). MR 0448949
[3] J. Haslinger I. Hlaváček: Convergence of finite element method based on the dual variational formulation. Apl. Mat. 21 1976, 43 - 65. MR 0398126
[4] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Academia, Prague 1967. MR 0227584
[5] J. Haslinger: Finite element analysis for unilateral problems with obstacles on the boundary. Apl. Mat. 22 1977, 180-189. MR 0440956 | Zbl 0434.65083
[6] J. Haslinger: A note on a dual finite element method. CMUC 17, 4 1976, 665 - 673. MR 0431750 | Zbl 0361.65095
[7] P. G. Ciarlet P. A. Raviart: General Lagrange and Herniite interpolation in $R^n$ with applications to finite element methods. Arch. Rational Mech. Anal. 46 1972, 217-249. MR 0336957
[8] J. Cea: Optimisation, théorie et algorithmes. Dunod, Paris 1971. MR 0298892 | Zbl 0211.17402
[9] G. Strang: Approximations in the finite element method. Numer. Math. 19, 81 - 98. DOI 10.1007/BF01395933 | MR 0305547
[10] J. L. Lions: Quelques Méthodes de résolution des problèmes aux limites non linéaires. Dunod, Paris. Zbl 0248.35001
[11] P. A. Raviart: Hybrid finite element methods for solving 2nd order elliptic equations. Conference on Numer. Analysis, Dublin, 1974.
[12] I. Hlaváček: Dual finite element analysis for unilateral boundary value problems. Apl. Mat. 22 1977, 14-51. MR 0426453
[13] I. Hlaváček: Dual finite element analysis for elliptic problems with obstacles on the boundary, I. Ap. Mat. 22 (1977), 244-255. MR 0440958
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