@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: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {711--748}, publisher = {AFCET - Gauthier-Villars}, address = {Paris}, volume = {25}, number = {6}, year = {1991}, mrnumber = {1135991}, zbl = {0737.76045}, language = {en}, url = {http://archive.numdam.org/item/M2AN_1991__25_6_711_0/} }
TY - JOUR AU - Gunzburger, M. D. AU - Hou, L. S. AU - Svobodny, Th. P. TI - Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with Dirichlet controls JO - ESAIM: Modélisation mathématique et analyse numérique PY - 1991 SP - 711 EP - 748 VL - 25 IS - 6 PB - AFCET - Gauthier-Villars PP - Paris UR - http://archive.numdam.org/item/M2AN_1991__25_6_711_0/ LA - en ID - M2AN_1991__25_6_711_0 ER -
%0 Journal Article %A Gunzburger, M. D. %A Hou, L. S. %A Svobodny, Th. P. %T Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with Dirichlet controls %J ESAIM: Modélisation mathématique et analyse numérique %D 1991 %P 711-748 %V 25 %N 6 %I AFCET - Gauthier-Villars %C Paris %U http://archive.numdam.org/item/M2AN_1991__25_6_711_0/ %G en %F 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: Modélisation mathématique et analyse numérique, Tome 25 (1991) no. 6, pp. 711-748. http://archive.numdam.org/item/M2AN_1991__25_6_711_0/
[1] On some control problems in fluid mechanics. Theoret. Comput. Fluid Dynamics. To appear. | Zbl
and ,[2] Sobolev Spaces. Academic, New York, 1975. | MR | Zbl
,[3] The finite element method with Lagrange multipliers. Numer. Math. 16 179-192, 1973. | MR | Zbl
,[4] 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
and ,[5] 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] 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] Finite-dimensional approximation of nonlinear problem. Part I : branches of nonsingular solutions. Numer. Math. 36 1-25, 1980. | MR | Zbl
, and ,[8] 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] The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam, 1978. | MR | Zbl
,[10] Approximation des problèmes faiblement non linéaires. To appear.
,[11] Finite Element Methods for Navier-Stokes Equations. Springer, Berlin, 1986. | MR | Zbl
and ,[12] Finite Element Methods for Incompressible Viscous Flows :A Guide to Theory, Practice and Algorithms. Academic, Boston, 1989. | MR
,[13] Treating inhomogeneous essential boundary conditions in finite element methods. SIAM J. Num. Anal., To appear. | MR
, ,[14] Boundary velocity control of incompressible flow with an application to viscous drag reduction. SIAM J. Opt. Contr., To appear. | MR | Zbl
, and ,[15] 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
, and ,[16] 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] Some Aspects of the Optimal Control of Distributed Parameter Systems. SIAM, Philadelphia, 1972. | Zbl
,[18] Principles of Functional Analysis. Academic, New York, 1971. | MR | Zbl
,[19] 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] Navier-Stokes Equations. North-Holland, Amsterdam, 1979. | MR | Zbl
,[21] Navier-Stokes Equations and Nonlinear Functional Analysis. SIAM, Philadelphia, 1983. | MR | Zbl
,[22] Finite element approximation of incompressible Navier-Stokes equations with slip boundary condition. Numer. Math. 50 697-621, 1987. | MR | Zbl
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