Least-squares methods for Navier-Stokes boundary control problems

International Journal of Computational Fluid Dynamics

Volumn 9, Issue 1, 1998, Pages 43-58

  Bochev, P B ^a   Bedivan, D M ^a  

^a UNIVERSITY OF TEXAS AT ARLINGTON   (United States)

Author keywords

Least squares; Navier Stokes equations; Optimal control

Indexed keywords

EID: 3142619678     PISSN: 10618562     EISSN: None     Source Type: Journal    
DOI: 10.1080/10618569808940839     Document Type: Article

References (25)

1. Bedivan, D. and Fix, G. J. (1995). Least-squares methods for optimal shape design problems, Computers Math. Applic., 30(2), pp. 17-25.
2. Bochev, P. (1997). Analysis of least-squares methods for the Navier-Stokes equations, to appear in SIAM J. Num. Anal., 34/5.
3. Bochev, P. and Gunzburger, M. (1993). Accuracy of least-squares method for the Navier-Stokes equations, Comput. and Fluids, 22(4/5), 549-563.
4. Bochev, P. and Gunzburger, M. (1994). Analysis of least-squares finite element methods for the Stokes equations, Math. Comp., 63(208), pp. 479-506.
5. Bochev, P., Cai, Z., Manteuffel, T. and McCormick, S. Analysis of least-squares principles for the Navier-Stokes equations, to appear in SIAM J. Num. Anal.
6. Borggaard, J., Burkardt, J., Gunzburger, M. and Peterson, J. (1994). Editors, Optimal design and control, Proceedings of the Workshop on Optimal Design and Control, Blacksburg, VA; Birkhauser.
7. Bramble, J. H., Lazarov, R. D. and Pasciak, J. E. (1994). A least-squares approach based on a discrete minus one inner produce for first order systems, Mathematical Science Institute, Cornell University, Technical report 94-32, 23 pages.
8. Brezzi, F., Rappaz, J. and Raviart, P.-A. (1980). Finite-dimensional approximation of nonlinear problems, Part I: Branches of nonsingular solutions, Numer. Math., 36, pp. 1-25.
9. Chang, C. L. and Jiang, B. N. (1990). An error analysis of least squares finite element method of velocity-pressure-vorticity formulation for Stokes problem, Comp. Meth. Appl. Mech. Engrg., 84, pp. 247-255.
10. Desai, M. and Ito, K. (1994). Optimal Control of Navier-Stokes Equations, SIAM J. Control and Optim., 32, pp. 1428-1446.
11. Fernandez Cara, E. (1989). Optimal design in fluid mechanics. The finite element approach, in: Proc. IFIP WG. 72 Working Conference, Santiago de Compostela 1987, edited by A. Bermudez, Springer, pp. 120-131.
12. Ghia, U., Ghia, K. N. and Shin, C. T. (1982). High-Resolutions for incompressible flow using the Navier-Stokes equations and a multigrid method, J. Comp. Phys., 48, pp. 387-411.
13. 3, Math. Comp., 51(433), pp. 55-74.
14. Girault, V. and Raviart, P.-A. (1986). finite Element Methods for Navier-Stokes Equations, Springer, Berlin.
15. Glowinski, R. and Pironneau, O. (1976). Toward the computation of minimum drag profiles in viscous laminar flow, Appl. Math. Model., 1, pp. 58-66.
16. Gunzburger, M, Hou, L. and Svobodny, T. (1992). Boundary velocity control of incompressible flow with an application to drag reduction, SIAM J. Control and Optim., 30, pp. 167-181.
17. Gunzburger, M. and Hou, L. (1996). Finite-dimensional approximation of a class of constrained non-linear optimal control problems, SIAM J. Control Optim., 34/3, 1001-1043.
18. Gunzburger, M. and Kim, H. Existence of an optimal solution of a shape control problem for the stationary Navier-Stokes equations, submitted.
19. Jiang, B.-N., Lin, T. and Povinelli, L. (1993). A least-squares finite element method for 3D incompressible Navier-Stokes equations, AIAA Report 93-0338.
20. Jiang, B.-N., Lin, T. and Povinelli, L. (1994). Large-scale computation of incompressible viscous flow by least-squares finite element method, Comput. Meth. Appl. Mech. Engrg., 114, pp. 213-231.
21. Jiang, B.-N. and Povinelli, L. (1993). Optimal least-squares finite element methods for elliptic problems. Comp. Meth. Appl. Engrg., 102, 199-212.
22. Jiang, B.-N. and Povinelli, L. (1990). Least-squares finite element method for fluid dynamics, Comput. Meth. Appl. Mech. Engrg., 81, 13-37.
23. Jiang, B.-N., Loh, C. Y. and Povinelli, L. (1994). Theoretical study of the incompressible Navier-Stokes equations by the least squares method, NASA TM 106535, ICOMP-94-04, NASA Cleveland.
24. Lefebvre, D., Peraire, J. and Morgan, K. (1992). Least-squares finite element solution of compressible and incompressible flows, Int. J. Num. Meth. Heat Fluid Flow, 2, 99-113.
25. Wendland, W. (1979). Elliptic Systems in the Plane, Pitman, London.