An equivalent formulation for variational problems with constraints
Palabras clave:
Funciones, Elementos finitos
Resumen
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.Citas
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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.
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.
Publicado
2018-04-02
Cómo citar
Gatica, G. (2018). An equivalent formulation for variational problems with constraints. Proyecciones. Revista De Matemática, 8(16), 17-39. https://doi.org/10.22199/S07160917.1990.0016.00002
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