×

Application de la méthode des éléments finis à l’approximation d’un problème de domaine optimal. Méthodes de résolution des problèmes approches. (French) Zbl 0323.90063


MSC:

90C90 Applications of mathematical programming
90C30 Nonlinear programming
74S05 Finite element methods applied to problems in solid mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] D. Begis, R. Glowinski,Some numerical problems in optimal control of distributed parameter systems connected with variational inequalities and optimization of a domain. Proceedings of the 1972 IEEE Conference on Decision and Control and XIth Symposium on Adaptative Processes, Dec. 13-15, New Orleans, Louisiana, pp. 366-369.
[2] D. Begis, R. Glowinski,Application de la méthode des éléments finis à la résolution d’un problème de domaine optimal. Dans Computing Methods in Applied Sciences and Engineering, Part 2, R. Glowinski & J.L. Lions, Ed. Lecture Notes in Computer Science, 11, Springer-Verlag, (1974), pp. 403-434. · Zbl 0289.49040
[3] J. L. Lions,Some aspects of the optimal control of distributed systems. Regional Conference Series in Applied Math. SIAM Publication N{\(\deg\)} 6, 1972. · Zbl 0275.49001
[4] J. L. Lions,On the optimal control of distributed parameter systems Dans Techniques of Optimization, A. V. Balakrishnan Ed., Academic Press (1972), pp. 137-158.
[5] J. Cea,Adaptation de la méthode du gradient à un problème d’identification de domaine. Dans Computing Methods in Applied Sciences and Engineering, Part 2, R. Glowinski et J. L. Lions, Ed. Lecture Notes in Computer Science, 11, Springer-Verlag, (1974), pp. 391-402. · Zbl 0304.93011
[6] O. Pironneau,On optimum profiles in Stokes flow. J. of Fluid Mechanics (1973), Vol. 59, Part 1, pp. 117-128; · Zbl 0274.76022
[7] Ph.Morice,Une méthode d’optimisation de forme de domaine. Application à l’écoulement stationnaire à travers une digue poreuse. Lecture Notes in Economics and Mathematical Systems, 107, pp. 454-467. · Zbl 0376.76072
[8] K. Yosida,Functional Analysis, Springer-Verlag, 1965. · Zbl 0126.11504
[9] J. L. Lions,Problèmes aux limites dans les équations aux dérivées partielles, Presses de l’Université de Montréal, 1962.
[10] J. Necas,Les Méthodes directes en théorie des équations aux dérivées partielles. Masson, 1967.
[11] J. L. Lions, Communication personnelle. · Zbl 0595.35043
[12] G. Chavent,Analyse fonctionnelle et identification de coefficients répartis dans les équations aux dérivées partielles. Thèse d’Etat, Université de Paris VI, 1971. · Zbl 0226.35006
[13] P. G. Ciarlet, P. A. Raviart,Interpolation Theory over curved elements with applications to finite element methods. Computer Methods Applied Mechanics and Engineering, Vol. 1 (1972), pp. 217-249. · Zbl 0261.65079
[14] P. G. Ciarlet,Orders of convergence in finite element methods. Dans The Mathematics of finite elements and Applications, J. R. Whiteman Ed., Academic Press (1973), pp. 113-129. · Zbl 0291.65024
[15] R. Glowinski,Approximations externes, par éléments finis de Lagrange, d’ordre un et deux, du problème de Dirichlet pour l’opérateur biharmonique. Méthode itérative de résolution des problèmes approchés. Dans Topics in Numerical Analysis, J. J. H. Miller Ed., Academic Press, (1973), pp. 123-171.
[16] R. Glowinski, J. L. Lions, R. Tremolieres,Analyse Numérique des Inéquations Variationnelles, t. 1, DUNOD, à paraître.
[17] J. Cea,Optimisation. Théorie et Algorithmes. Dunod (1974).
[18] C. Baiocchi, V. Comincioli, L. Guerri, G. Volpi,Free boundary problems in the theory of fluid flow through porous media: a numerical approach. Calcolo X (1973), pp. 1-86. · Zbl 0296.76052
[19] C. Baiocchi, V. Comincioli, E. Magenes, G. A. Pozzi,Free boundary problems in the theory of fluid flow through porous media: existence and uniqueness theorems. Ann. di Matematica XCVII, (1973), pp. 1-82. · Zbl 0343.76036
[20] C. Baiocchi, Communication au Congrès International des Mathématiciens, Vancouver, Août 1974.
[21] V. Comincioli,On some oblique derivative problems arising in the fluid flow in porous media. A theoretical and numerical approach. Applied Mathematics and Optimization. An Int. J. Vol. 1, No. 3 (1974), pp. 35-46.
[22] A. Bensoussan, J. L. Lions,Nouvelles Méthodes en contrôle impulsionnel. Applied Mathematics and Optimization. An Int. J. Vol. 1 no 3, (1974), pp. 10-34.
[23] J. T. Oden, O. C. Zienkiewicz, R. H. Gallagher, C. Taylor, Ed.,Finite element in flow problems. University of Alabama Press, 1974.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.