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Solution of the 3-D stationary euler equation by optimal control methods

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Control Problems for Systems Described by Partial Differential Equations and Applications

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 97))

Abstract

An hyperbolic nonlinear PDE arising in turbulence is solved by the techniques of optimal control theory because of its non standard boundary conditions. Because there are 4 unknown functions of 3 variables, this method of solution yieldsextremely large optimal control problems. Conjugate Gradient Algorithms and Finite Element Discretization where employed with satisfactory results. However, a Quasi-Newton method failed to improve computer time.

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References

  1. C. Bègue, O. Pironneau: Hyperbolic systems with periodic boundary conditions, Comp. & Maths with Appls., Vol. 11, Nos. 1–3, pp.113–128, (1985).

    Google Scholar 

  2. M.O. Bristeau, R. Glowinski, B. Mantel, J. Périaux, P. Perrier: Finite Element Methods for Solving the Navier-Stokes Equations for Compressible Unsteady Flows, Proc. of 5th International Conference on Finite Element and Flow Problems, University of Texas at Austin, U.S.A., 1984 (CAREY G.F. & ODEN J.T. Eds., pp. 449–462).

    Google Scholar 

  3. A. Buckley, A. Lenir: On-Like variable storage conjugate gradients. Mathematical Programming 27, 2, pp. 155–175 (1983).

    Google Scholar 

  4. R. Glowinski: Numerical Methods for Nonlinear Variational Problems, Springer-Verlag, New-York, 1984.

    Google Scholar 

  5. R. Glowinski, O. Pironneau: On a mixed finite element approximation of the Stokes problem (I). Numer. Math. 33, 397–424 (1979).

    Google Scholar 

  6. J.L. Lions: Control Optimal des Systèmes gouvernés par des E.D.P. Dunod, Paris (1968).

    Google Scholar 

  7. D.W. McLaughin, G. Papanicolaou and O. Pironneau: Convection of Microstructure and related problems. SIAM Appl. Math., Vol. 45, No. 5, Oct. 85.

    Google Scholar 

  8. S.A. Orszag: Numerical simulation of the Taylor Green Vortex (Edited by R. Glowinski), Lecture Notes in Computer Sciences, Vol. 11, Part 2, p. 50, Springer Verlag, Berlin (1974).

    Google Scholar 

  9. O. Pironneau: Optimal Shape design for elliptic systems. Springer Series in Comp. Physics, 1983.

    Google Scholar 

  10. E. Polak: Computational Methods in Optimization. Academic Press (1971).

    Google Scholar 

  11. F. Thomasset: Finite Element Solutions of the Navier-Stokes Equations. Springer Series in Comp. Physics (1980).

    Google Scholar 

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Author information

Authors and Affiliations

  1. University of Sevilla, Spain

    T. Chacon

  2. University of Paris; INRIA, Rocquencourt, France

    O. Pironneau

Authors
  1. T. Chacon
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  2. O. Pironneau
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Irena Lasiecka Roberto Triggiani

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© 1987 International Federation for Information Processing

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Chacon, T., Pironneau, O. (1987). Solution of the 3-D stationary euler equation by optimal control methods. In: Lasiecka, I., Triggiani, R. (eds) Control Problems for Systems Described by Partial Differential Equations and Applications. Lecture Notes in Control and Information Sciences, vol 97. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0038751

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  • DOI: https://doi.org/10.1007/BFb0038751

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18054-8

  • Online ISBN: 978-3-540-47722-8

  • eBook Packages: Springer Book Archive

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