Free access
Issue
ESAIM: M2AN
Volume 34, Number 6, November/December 2000
Page(s) 1233 - 1258
DOI http://dx.doi.org/10.1051/m2an:2000125
Published online 15 April 2002
  1. F. Abergel and R. Temam, On some control problems in fluid mechanics. Theor. Comp. Fluid Dyn. 1 (1990) 303-326. [CrossRef]
  2. R. Adams, Sobolev Spaces. Academic Press, New York (1975).
  3. V. Alekseev, V. Tikhomirov and S. Fomin, Optimal Control. Consultants Bureau, New York (1987).
  4. G. Armugan and O. Pironneau, On the problem of riblets as a drag reduction device. Optimal Control Appl. Methods 10 (1989) 93-112. [CrossRef] [MathSciNet]
  5. I. Babuska, The finite element method with Lagrangian multipliers. Numer. Math. 16 (1973) 179-192. [CrossRef]
  6. D. Bedivan, Existence of a solution for complete least squares optimal shape problems. Numer. Funct. Anal. Optim. 18 (1997) 495-505. [CrossRef] [MathSciNet]
  7. D. Bedivan and G. Fix, An extension theorem for the space Hdiv. Appl. Math. Lett. (to appear).
  8. D. Begis and R. Glowinski, Application de la méthode des éléments finis à l'approximation d'un problème de domaine optimal. Méthodes de résolution des problèmes approchés. Appl. Math. Optim. 2 (1975) 130-169. [CrossRef] [MathSciNet]
  9. D. Chenais, On the existence of a solution in a domain identification problem. J. Math. Anal. Appl. 52 (1975) 189-219. [CrossRef] [MathSciNet]
  10. P. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1978).
  11. P. Ciarlet, Introduction to Numerical Linear Algebra and Optimization. Cambridge University, Cambridge (1989).
  12. E. Dean, Q. Dinh, R. Glowinski, J. He, T. Pan and J. Periaux, Least squares domain embedding methods for Neumann problems: applications to fluid dynamics, in Domain Decomposition Methods for Partial Differential Equations, D. Keyes et al. Eds., SIAM, Philadelphia (1992).
  13. N. Di Cesare, O. Pironneau and E. Polak, Consistent approximations for an optimal design problem. Report 98005, Labotatoire d'Analyse Numérique, Paris (1998).
  14. N. Fujii, Lower semi-continuity in domain optimization problems. J. Optim. Theory Appl. 57 (1988) 407-422. [CrossRef]
  15. V. Girault and P. Raviart, The Finite Element Method for Navier-Stokes Equations: Theory and Algorithms. Springer, New York (1986).
  16. R. Glowinski, Numerical Methods for Nonlinear Variational Problems. Springer, New York (1984).
  17. R. Glowinski and O. Pironneau, Toward the computation of minimum drag profile in viscous laminar flow. Appl. Math. Model. 1 (1976) 58-66. [CrossRef]
  18. M. Gunzburger, L. Hou and T. Svobodny, Analysis and finite element approximations of optimal control problems for the stationary Navier-Stokes equations with Dirichlet controls. RAIRO Modél. Math. Anal. Numér. 25 (1991) 711-748. [MathSciNet]
  19. M. Gunzburger, L. Hou and T. Svobodny, Optimal control and optimization of viscous, incompressible flow, in Incompressible Computational Fluid Dynamics, M. Gunzburger and R. Nicolaides Eds., Cambridge University, New York (1993) 109-150.
  20. M. Gunzburger and H. Kim, Existence of a shape control problem for the stationary Navier-Stokes equations. SIAM J. Control Optim. 36 (1998) 895-909. [CrossRef] [MathSciNet]
  21. M. Gunzburger and S. Manservisi, Analysis and approximation of the velocity tracking problem for Navier-Stokes equations with distributed control. SIAM J. Numer. Anal. 37 (2000) 1481-1512. [CrossRef] [MathSciNet]
  22. M. Gunzburger and S. Manservisi, The velocity tracking problem for Navier-Stokes flows with bounded distributed control. SIAM J. Control Optim. 37 (1999) 1913-1945. [CrossRef] [MathSciNet]
  23. M. Gunzburger and S. Manservisi, A variational inequality formulation of an inverse elasticity problem. Comput. Methods Appl. Mech. Engrg. 189 (2000) 803-823. [CrossRef] [MathSciNet]
  24. M. Gunzburger and S. Manservisi, Some numerical computations of optimal shapes for Navier-Stokes flows (in preparation).
  25. J. Haslinger, K.H. Hoffmann and M. Kocvara, Control fictitious domain method for solving optimal shape design problems. RAIRO Modél. Math. Anal. Numér. 27 (1993) 157-182. [MathSciNet]
  26. J. Haslinger and P. Neittaanmaki, Finite Element Approximation for Optimal Shape, Material and Topology Design, 2nd edn. Wiley, Chichester (1996).
  27. K. Kunisch and G. Pensil, Shape optimization for mixed boundary value problems based on an embedding domain method (to appear).
  28. O. Pironneau, Optimal Shape Design in Fluid Mechanics. Thesis, University of Paris, France (1976).
  29. O. Pironneau, On optimal design in fluid mechanics. J. Fluid. Mech. 64 (1974) 97-110. [CrossRef] [MathSciNet]
  30. O. Pironneau, Optimal Shape Design for Elliptic Systems. Springer, Berlin (1984).
  31. R. Showalter, Hilbert Space Methods for Partial Differential Equations. Electron. J. Differential Equations (1994) http://ejde.math.swt.edu/mono-toc.html
  32. J. Simon, Domain variation for Stokes flow, in Lecture Notes in Control and Inform. Sci. 159, X. Li and J. Yang Eds., Springer, Berlin (1990) 28-42.
  33. J. Simon, Domain variation for drag Stokes flows, in Lecture notes in Control and Inform. Sci. 114, A. Bermudez Ed., Springer, Berlin (1987) 277-283.
  34. T. Slawig, Domain Optimization for the Stationary Stokes and Navier-Stokes Equations by Embedding Domain Technique. Thesis, TU Berlin, Berlin (1998).
  35. J. Sokolowski and J. Zolesio, Introduction to Shape Optimization: Shape Sensitivity Analysis. Springer, Berlin (1992).
  36. S. Stojanovic, Non-smooth analysis and shape optimization in flow problems. IMA Preprint Series 1046, IMA, Minneapolis (1992).
  37. R. Temam, Navier-Stokes equation. North-Holland, Amsterdam (1979).
  38. R. Temam, Navier-Stokes equations and Nonlinear Functional Analysis. SIAM, Philadelphia (1993).
  39. V. Tikhomirov, Fundamental Principles of the Theory of Extremal Problems. Wiley, Chichester (1986).

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