Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with Dirichlet controls
M2AN - Modélisation mathématique et analyse numérique, Volume 25 (1991) no. 6, pp. 711-748.
@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 = {M2AN - Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {711--748},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {25},
     number = {6},
     year = {1991},
     zbl = {0737.76045},
     mrnumber = {1135991},
     language = {en},
     url = {http://archive.numdam.org/item/M2AN_1991__25_6_711_0/}
}
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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. M2AN - Modélisation mathématique et analyse numérique, Volume 25 (1991) no. 6, pp. 711-748. http://archive.numdam.org/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

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

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

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

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

[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 | Zbl

[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 | Zbl

[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

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

[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

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

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

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