Geveci, Tunc On the approximation of the solution of an optimal control problem governed by an elliptic equation. (English) Zbl 0426.65067 RAIRO, Anal. Numér. 13, 313-328 (1979). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 89 Documents MSC: 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 49J20 Existence theories for optimal control problems involving partial differential equations 65N15 Error bounds for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations Keywords:error estimates; approximate solutions; optimal control problem; Neumann problem; saddle point; Fenchel-Rockafellar duality theory PDF BibTeX XML Cite \textit{T. Geveci}, RAIRO, Anal. Numér. 13, 313--328 (1979; Zbl 0426.65067) Full Text: DOI EuDML OpenURL References: [1] 1. P. G. CIARLET and P. A. RAVIART, General Lagrange and Hermite interpolation in \(R^n\) with applications to finite element methods, Arc. Rat. Mech. Anal., Vol. 46, 1972, pp. 177-199. Zbl0243.41004 MR336957 · Zbl 0243.41004 [2] 2. I. EKELAND and R. TEMAM, Convex Analysis and Variational Problems, North-Holland, Amsterdam, 1976. Zbl0322.90046 MR463994 · Zbl 0322.90046 [3] 3. R. S. FALK, Approximation of a Class of Optimal Control Problems with Order of Convergence Estimates, J. Math. Anal. Appl., Vol. 44, 1973, pp. 28-47. Zbl0268.49036 MR686788 · Zbl 0268.49036 [4] 4. R. GLOWINSKI, Introduction to the Approximation of Elliptic Variational Inequalities, Université Paris-VI, Laboratoire Analyse numérique, Vol. 189, Paris, 1976. [5] 5. P. GRISVARD, Behaviour of Solutions of an Elliptic Boundary Value Problem in a Polygonal or Polyhedral Domain, SYNSPADE, 1974, B. HUBBARD, Ed., pp. 207-274, Academic Press, New York, 1976. Zbl0361.35022 MR466912 · Zbl 0361.35022 [6] 6. W. W. HAGER and K. MITTER, Lagrange Duality for Convex Control Problems, S.I.A.M. J. Control, Vol. 14, 1976, pp. 842-856. Zbl0336.49007 · Zbl 0336.49007 [7] 7. O. A. LADYZHENSKAYA and N. N. URAL’TSEVA, Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1968. Zbl0164.13002 MR244627 · Zbl 0164.13002 [8] 8. I. LASIECKA and K. MALANOWSKI, On Regularity of Solutions to Convex Optimal Control Problems with Control Constraints for Parabolic Systems, Control and Cybernetics, Vol. 6, 1977, pp. 57-74. Zbl0365.49003 MR467439 · Zbl 0365.49003 [9] 9. I. LASIECKA and K. MALANOWSKI, On discrete-Time Ritz-Galerkin Approximation of Control Constrained Optimal Control Problems for Parabolic Systems, Control and Cybernetics, Vol. 7, 1978, pp. 21-36. Zbl0459.49022 MR484630 · Zbl 0459.49022 [10] 10. A. LEWY and G. STAMPACCHIA, On the Regularity of the Solution of a Variational Inequality, Comm. Pure Appl. Math., Vol. 22, 1969, pp. 153-188. Zbl0167.11501 MR247551 · Zbl 0167.11501 [11] 11. J.-L. LIONS, Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, Berlin, 1971. Zbl0203.09001 MR271512 · Zbl 0203.09001 [12] 12. J. MOSSINO, An Application of Duality to Distributed Optimal Control Problems with Constraints on the Control and the State, J. Math. Anal. Appl., Vol. 50, 1975, pp. 223-242. Zbl0304.49003 MR385670 · Zbl 0304.49003 [13] 13. M. M. MOUSSAOUI, Régularité de la solution d’un problème à dérivée oblique, C. R. Acad. Sc, Paris, Vol. 279, série A, 1974, pp. 869-872. Zbl0293.35014 MR358062 · Zbl 0293.35014 [14] 14. J. T. ODEN and N. N. REDDY, An Introduction to the Mathematical Theory of Finite Elements, Wiley-Interscience, New York, 1976. Zbl0336.35001 MR461950 · Zbl 0336.35001 [15] 15. T. ROCKAFELLAR, State Constraints in Convex Control Problems of Bolza, S.I.A.M. J. Control, Vol. 10, 1972, pp. 691-715. Zbl0224.49003 MR324505 · Zbl 0224.49003 [16] 16. G. STAMPACCHIA, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier, Vol. 15, 1968, pp. 189-258. Zbl0151.15401 MR192177 · Zbl 0151.15401 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.