An equivalent formulation for variational problems with constraints

Gabriel N. Gatica


The main purpose of this paper is to reconsider the studying of existence, uniqueness and approximation of solution to a variational problem with constraints. Under certain assumptions on the bilinear forms involved it is proved that the original formulation is equivalent to a simplified version of it on smaller spaces. By applying the usual Brezzi's theory to this new formulation a modified Babuska-Brezzi condition is deduced.

Palabras clave

Funciones; Elementos finitos

Texto completo:



AUBIN, J. and BURCHARD, H.: Some aspects of the method of the hypercicle applied to elliptic variational problems. In SYNSPADE 1970, B. Hubbard, editor, Academic Press, New York, (1971).

AZIZ, A. and BABUSKA, I.: Survey lectures on the mathematical foundations of the finite element method. In the mathematical foundations of the finite element method with applications to partial differential equations , edit. by A. Aziz, Academic Press, New York, pp. 5-359, (1972).

BABUSKA, I.: Error bounds for finite element method. Numer. Mathem., vol. 16, pp . 322-333, (1972).

BABUSKA, I.: The finite element method with Lagrangian multipliers. Numer. Mathem., vol. 20, pp. 179-192, (1973).

BABUSKA, I.; ODEN, J. T. and LEE, J. K.: Mixed-hybrid finite element approximations of second order elliptic boundary value problems. Comput. Meth. Appl. Mech. Eng., vol. 11, pp. 175-206, (1977).

BREZZI, F. : On the existence, uniqueness and approximation of saddlepoint problems arising from Lagrangian multipliers. RAIRO, 8 - R2, pp. 129-151, (1974).

CIARLET, P.: The finite element method for elliptic problems. North-Holland Publishing Company, 1978.

KUFNER, A.; JOHN, O. and FUCIK, S. : Function spaces. Prague, Academia, 1977 .

NICOLAIDES, R.A.: Existence, uniqueness and approximation for generalized saddle-point problems. SIAM Jour. Numer. Anal., vol. 19, 2, pp. 349-357, (1982).

ODEN, J.T. and CAREY, G.: Finite elements: mathematical aspects, vol. IV, Prentice-Hall, 1983.


Enlaces refback

  • No hay ningún enlace refback.