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2007 | 5 | 4 | 751-763
Tytuł artykułu

A Numerical Approach of the sentinel method for distributed parameter systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we consider the problem of detecting pollution in some non linear parabolic systems using the sentinel method. For this purpose we develop and analyze a new approach to the discretization which pays careful attention to the stability of the solution. To illustrate convergence properties we give some numerical results that present good properties and show new ways for building discrete sentinels.
Wydawca
Czasopismo
Rocznik
Tom
5
Numer
4
Strony
751-763
Opis fizyczny
Daty
wydano
2007-12-01
online
2007-12-01
Twórcy
autor
Bibliografia
  • [1] A.S. Ackleh, B.G. Fitzpatrick and T.G. Hallam: “Approximation and parameter estimation problems for algal aggregation models”, Math. Models Methods Appl. Sci., Vol. 4, (1994), no. 3, pp. 291–311. http://dx.doi.org/10.1142/S0218202594000182
  • [2] P. Bochev and M.D. Gunzburger: “Least-squares finite-element methods for optimization and control problems for the Stokes equations”, Comput. Math. Appl., Vol. 48, (2004), no. 7–8, pp. 1035–1057. http://dx.doi.org/10.1016/j.camwa.2004.10.004
  • [3] O. Bodart, J.P. Kernévez and T. Männikkö: “Sentinels for distributed environmental systems”, In Eleventh IASTED International Conference on Modelling, Identification and Control, Innsbruck (Austria), (1992), pp. 219–222.
  • [4] O. Bodart, J.P. Kernévez and T. Männikkö: “Numerical methods to compute sentinels for distributed systems”, In: J. Yvon, J. Henry (Eds.), Proceedings of the 16th IFIP TC7 conference on System modelling and Optimization, Springer Verlag, Paris, 1994.
  • [5] J.H. Bramble, A.H. Schatz, V. Thomée and L.B. Wahlbin: “Some convergence estimates for semidiscrete Galerkin type approximations for parabolic equations”, SIAM J. Numer. Anal., Vol. 14, (1977), no. 2, pp. 218–241. http://dx.doi.org/10.1137/0714015
  • [6] H. Brezis: Analyse fonctionnelle. Théorie et applications, Collection Mathématiques Appliquées pour la Maîtrise, Masson, Paris, 1983.
  • [7] A. E. Hamidi: Remarques sur les sentinelles pour les systèmes distribués, Prépublication du département de Mathématique, Université La Rochelle, 2001.
  • [8] J.P. Kernévez: Sentinelle pour veiller sur l’environnement, Collection RMA, Masson, Paris, 1997.
  • [9] J.P. Kernévez: The sentinel method and its application to environmental pollution problems, CRC Mathematical Modelling Series, CRC Press, Boca Raton, FL, 1997.
  • [10] S. Labbé and E. Trélat: “Uniform controllability of semidiscrete approximations of parabolic control systems”, Systems Control Lett., Vol. 55, (2006), no. 7, pp. 597–609. http://dx.doi.org/10.1016/j.sysconle.2006.01.004
  • [11] I. Lasiecka and R. Triggiani: Control theory for partial differential equations: continuous and approximation theories, I, Abstract parabolic systems, Encyclopedia of Mathematics and its Applications, Vol. 74, Cambridge University Press, Cambridge, 2000.
  • [12] J.L. Lions: Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués, Tome 1, Contrôlabilité exacte, Recherches en Mathématiques Appliquées 8, Masson, Paris, 1988.
  • [13] J.L. Lions: Sentinelles pour les systèmes distribués á données incomplètes, Recherches en Mathématiques Appliquées 21, Masson, Paris, 1992.
  • [14] T. Mannikkö and O. Bodart: “Parameter identification with the method of sentinels”, Proceedings of the Workshop on Optimization and Optimal Control (Jyväskylä, 1992), Report 58, Univ. Jyväskylä, Jyväskylä, (1993), pp. 97–107.
  • [15] V. Mikhaĭlov: Équations aux dérivées partielles, Translated from the Russian by Irina Petrova, Mir, Moscow, distributed by Imported Publications, Inc., Chicago, Ill., 1980.
  • [16] F. Molinet: Simulation numerique de problème d’écosystèmes. Sentimelle pour la detection de l’origine d’une pollution, Ph.D. dissertation, Université Louise Pasteur, Strasbourg, France, 1997.
  • [17] R. Mosé, M.E. Stoeckel, C. Poulard, P. Ackerer and F. Lehmann: “Transport parameters identification: application of the sentinel method”, Computational Geosciences, Vol. 4, (2000), pp. 251–273. http://dx.doi.org/10.1023/A:1011516101288
  • [18] O. Nakoulima: “A revision of Lions’s notion of sentinels”, preprint.
  • [19] L.N. Trefethen: Spectral methods in MATLAB, Software, Environments, and Tools, 10, SIAM, Philadelphia, PA, 2000.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-007-0031-3
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