Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with Dirichlet controls
Gunzburger, M. D. ; Hou, L. S. ; Svobodny, Th. P.
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 25 (1991), p. 711-748 / Harvested from Numdam
@article{M2AN_1991__25_6_711_0,
     author = {Gunzburger, M. D. and Hou, L. S. and Svobodny, Th. P.},
     title = {Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with Dirichlet controls},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {25},
     year = {1991},
     pages = {711-748},
     mrnumber = {1135991},
     zbl = {0737.76045},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1991__25_6_711_0}
}
Gunzburger, M. D.; Hou, L. S.; Svobodny, Th. P. Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with Dirichlet controls. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 25 (1991) pp. 711-748. http://gdmltest.u-ga.fr/item/M2AN_1991__25_6_711_0/

[1] F. Abergel and R. Temam, On some control problems in fluid mechanics. Theoret. Comput. Fluid Dynamics. To appear. | Zbl 0708.76106

[2] R. Adams, Sobolev Spaces. Academic, New York, 1975. | MR 450957 | Zbl 0314.46030

[3] I. Babuška, The finite element method with Lagrange multipliers. Numer. Math. 16 179-192, 1973. | MR 359352 | Zbl 0258.65108

[4] I. Babuška and A. Aziz, Survey lectures on the mathematical foundations of the finite element method. The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (Ed. by A. Aziz), Academic, New York, 3-359, 1973. | MR 421106 | Zbl 0268.65052

[5] F. Brezzi, On the existence, uniqueness, and approximation of saddle-point problems arising from Lagrange multipliers. RAIRO Model. Math. Anal Numér. 8-32, 129-151, 1974. | Numdam | MR 365287 | Zbl 0338.90047

[6] F. Brezzi, A survey of mixed finite element methods. Finite Elements, Theory and Application (Ed. by D. Dwoyer, M. Hussaini and R. Voigt), Springer, New York, 34-49, 1988. | MR 964479 | Zbl 0665.73058

[7] F. Brezzi, J. Rappaz andP.-A. Raviart, Finite-dimensional approximation of nonlinear problem. Part I : branches of nonsingular solutions. Numer. Math. 36 1-25, 1980. | MR 595803 | Zbl 0488.65021

[8] L. Cattabriga, SU un problema al contorno relativo al sistema di equazioni di Stokes. Rend. Sem. Mat. Univ. Padova 31 308-340, 1961. | Numdam | MR 138894 | Zbl 0116.18002

[9] P. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam, 1978. | MR 520174 | Zbl 0383.65058

[10] M. Crouzeix, Approximation des problèmes faiblement non linéaires. To appear.

[11] V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations. Springer, Berlin, 1986. | MR 851383 | Zbl 0585.65077

[12] M. Gunzburger, Finite Element Methods for Incompressible Viscous Flows :A Guide to Theory, Practice and Algorithms. Academic, Boston, 1989. | MR 1017032

[13] M. Gunzburger, L. Hou, Treating inhomogeneous essential boundary conditions in finite element methods. SIAM J. Num. Anal., To appear. | MR 1154272

[14] M. Gunzburger, L. Hou and T. Svobodny, Boundary velocity control of incompressible flow with an application to viscous drag reduction. SIAM J. Opt. Contr., To appear. | MR 1145711 | Zbl 0756.49004

[15] M. Gunzburger, L. Hou and T. Svobodny, Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with distributed and Neumann controls. Math. Comp. 57, 123-151, 1991. | MR 1079020 | Zbl 0747.76063

[16] L. Hou, Analysis and finite element approximation of some optimal control problems associated with the Navier-Stokes equations. Ph. D. Thesis, Carnegie Mellon University, Pittsburgh, 1989.

[17] J. Lions, Some Aspects of the Optimal Control of Distributed Parameter Systems. SIAM, Philadelphia, 1972. | Zbl 0275.49001

[18] M. Schecter, Principles of Functional Analysis. Academic, New York, 1971. | MR 445263 | Zbl 0211.14501

[19] J. Serrin, Mathematical principles of classical fluid mechanics. Handbüch der Physik VIII/1 (ed. by S. Flügge and C. Truesdell) Springer, Berlin, 125-263, 1959. | MR 108116

[20] R. Temam, Navier-Stokes Equations. North-Holland, Amsterdam, 1979. | MR 603444 | Zbl 0426.35003

[21] R. Temam, Navier-Stokes Equations and Nonlinear Functional Analysis. SIAM, Philadelphia, 1983. | MR 764933 | Zbl 0833.35110

[22] R. Verfürth, Finite element approximation of incompressible Navier-Stokes equations with slip boundary condition. Numer. Math. 50 697-621, 1987. | MR 884296 | Zbl 0596.76031