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
[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
[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