Free Access
Issue
ESAIM: M2AN
Volume 34, Number 6, November/December 2000
Page(s) 1233 - 1258
DOI https://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] [EDP Sciences] [Google Scholar]
  2. R. Adams, Sobolev Spaces. Academic Press, New York (1975). [Google Scholar]
  3. V. Alekseev, V. Tikhomirov and S. Fomin, Optimal Control. Consultants Bureau, New York (1987). [Google Scholar]
  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] [Google Scholar]
  5. I. Babuska, The finite element method with Lagrangian multipliers. Numer. Math. 16 (1973) 179-192. [CrossRef] [Google Scholar]
  6. D. Bedivan, Existence of a solution for complete least squares optimal shape problems. Numer. Funct. Anal. Optim. 18 (1997) 495-505. [CrossRef] [MathSciNet] [Google Scholar]
  7. D. Bedivan and G. Fix, An extension theorem for the space Hdiv. Appl. Math. Lett. (to appear). [Google Scholar]
  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] [Google Scholar]
  9. D. Chenais, On the existence of a solution in a domain identification problem. J. Math. Anal. Appl. 52 (1975) 189-219. [CrossRef] [MathSciNet] [Google Scholar]
  10. P. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1978). [Google Scholar]
  11. P. Ciarlet, Introduction to Numerical Linear Algebra and Optimization. Cambridge University, Cambridge (1989). [Google Scholar]
  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). [Google Scholar]
  13. N. Di Cesare, O. Pironneau and E. Polak, Consistent approximations for an optimal design problem. Report 98005, Labotatoire d'Analyse Numérique, Paris (1998). [Google Scholar]
  14. N. Fujii, Lower semi-continuity in domain optimization problems. J. Optim. Theory Appl. 57 (1988) 407-422. [CrossRef] [Google Scholar]
  15. V. Girault and P. Raviart, The Finite Element Method for Navier-Stokes Equations: Theory and Algorithms. Springer, New York (1986). [Google Scholar]
  16. R. Glowinski, Numerical Methods for Nonlinear Variational Problems. Springer, New York (1984). [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  24. M. Gunzburger and S. Manservisi, Some numerical computations of optimal shapes for Navier-Stokes flows (in preparation). [Google Scholar]
  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] [Google Scholar]
  26. J. Haslinger and P. Neittaanmaki, Finite Element Approximation for Optimal Shape, Material and Topology Design, 2nd edn. Wiley, Chichester (1996). [Google Scholar]
  27. K. Kunisch and G. Pensil, Shape optimization for mixed boundary value problems based on an embedding domain method (to appear). [Google Scholar]
  28. O. Pironneau, Optimal Shape Design in Fluid Mechanics. Thesis, University of Paris, France (1976). [Google Scholar]
  29. O. Pironneau, On optimal design in fluid mechanics. J. Fluid. Mech. 64 (1974) 97-110. [CrossRef] [MathSciNet] [Google Scholar]
  30. O. Pironneau, Optimal Shape Design for Elliptic Systems. Springer, Berlin (1984). [Google Scholar]
  31. R. Showalter, Hilbert Space Methods for Partial Differential Equations. Electron. J. Differential Equations (1994) http://ejde.math.swt.edu/mono-toc.html [Google Scholar]
  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. [Google Scholar]
  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. [Google Scholar]
  34. T. Slawig, Domain Optimization for the Stationary Stokes and Navier-Stokes Equations by Embedding Domain Technique. Thesis, TU Berlin, Berlin (1998). [Google Scholar]
  35. J. Sokolowski and J. Zolesio, Introduction to Shape Optimization: Shape Sensitivity Analysis. Springer, Berlin (1992). [Google Scholar]
  36. S. Stojanovic, Non-smooth analysis and shape optimization in flow problems. IMA Preprint Series 1046, IMA, Minneapolis (1992). [Google Scholar]
  37. R. Temam, Navier-Stokes equation. North-Holland, Amsterdam (1979). [Google Scholar]
  38. R. Temam, Navier-Stokes equations and Nonlinear Functional Analysis. SIAM, Philadelphia (1993). [Google Scholar]
  39. V. Tikhomirov, Fundamental Principles of the Theory of Extremal Problems. Wiley, Chichester (1986). [Google Scholar]

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