Dynamics and approximations of a velocity tracking problem for the Navier-Stokes flows with piecewise distributed controls

SIAM Journal on Control and Optimization

Volumn 35, Issue 6, 1997, Pages 1847-1885

  Hou, L S ^a   Yan, Y ^b  

^a YORK UNIVERSITY   (Canada)

^b VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

Author keywords

Fully discrete approximations; Navier Stokes equations; Optimal control; Semidiscrete approximations

Indexed keywords

APPROXIMATION THEORY; DISTRIBUTED PARAMETER CONTROL SYSTEMS; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; PIECEWISE LINEAR TECHNIQUES; PROBLEM SOLVING; VELOCITY CONTROL;

FULLY DISCRETE APPROXIMATIONS; SEMI DISCRETE APPROXIMATIONS; VELOCITY TRACKING PROBLEM;

OPTIMAL CONTROL SYSTEMS;

EID: 0031271271     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S036301299529286X     Document Type: Article

References (18)

1. R. ADAMS, Sobolev Spaces, Academic Press, New York, 1975.
2. F. ABERGEL AND R. TEMAM, On some control problems in fluid mechanics, Theoret. Comput. Fluid Dynamics, 1 (1990) pp. 303-325.
3. H. CHOI, R. TEMAM, P. MOIN, AND J. KIM, Feedback control for unsteady flow and its application to the stochastic Burgers equation, J. Fluid Mech., 253 (1993), pp. 509-543.
4. P. CIARLET, Finite Element Methods for Elliptic Problems, North-Holland, Amsterdam, 1978.
5. P. CONSTANTIN AND C. FOIAS, Navier-Stokes Equations, University of Chicago, Chicago, 1988.
6. A. FURSIKOV, On some control problems and results concerning the unique solvability of a mixed boundary value problems for the three-dimensional Navier-Stokes and Euler systems, Soviet Math. Dokl., 3 (1980), pp. 889-893.
7. A. FURSIKOV, Control problems and theorems concerning the unique solvability of a mixed boundary value problems for the three-dimensional Navier-Stokes and Euler equations, Math USSR Sb., 43 (1982), pp. 281-307.
8. A. FURSIKOV, Properties of solutions of some extremal problems connected with the Navier-Stokes system, Math USSR Sb., 46 (1983), pp. 323-351.
9. A. FURSICOV, M. GUNZBURGER, AND L. HOU, Boundary value problems and optimal boundary control for the Navier-Stokes systems: The two-dimensional case, SIAM J. Control Optim., 36 (1998), to appear.
10. M. GUNZBURGER AND L. HOU, Treating inhomogeneous essential boundary conditions in finite element methods and the calculation of boundary stresses, SIAM J. Numer. Anal., 29 (1992), pp. 390-424.
11. 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 (1991), pp. 123-151.
12. V. GIRAULT AND P. RAVIART, Finite Element Methods for Navier-Stokes Equations, Springer-Verlag, Berlin, 1986.
13. J. HEYWOOD AND R. RANACKER, Finite element approximations of the nonstationary Navier-Stokes problem, IV, Error analysis for second order time discretization, SIAM J. Numer. Anal., 27 (1990), pp. 353-384.
14. L. HOU, S. RAVINDRIN, AND Y. YAN, Numerical solutions of optimal distributed control problems for incompressible flows, Internat. J. Comput. Fluid Dynamics, 8 (1997), pp. 99-114.
15. L. HOU AND Y. YAN, Dynamics for controlled Navier-Stokes systems with distributed control, SIAM J. Control Optim., 35 (1997), pp. 654-677.
16. J.-L. LIONS, Control of Distributed Singular Systems, Bordas, Paris, 1985.
17. S.S. RAVINDRAN, A Computational Study of Some Control Problems in Electrically Conducting Flows, Ph.D. thesis, Simon Fraser University, Burnaby, BC, Canada, 1994.
18. R. TEMAM, Navier-Stokes Equations, Theory and Numerical Methods, North-Holland, Amsterdam, 1983.