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Approximation of a class of optimal control problems with order of convergence estimates. (English) Zbl 0268.49036


MSC:

49M15 Newton-type methods
41A25 Rate of convergence, degree of approximation
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References:

[1] Babuška, I., Numerical solution of boundary value problems by the perturbed variational principle, University of Maryland Tech. Note BN-624 (1969)
[2] Bossavit, A., A linear control problem for a system governed by a partial differential equation, (Computing Methods in Optimization Problems, Vol. 2 (1969), Academic Press: Academic Press New York) · Zbl 0239.49003
[3] Bramble, J. H.; Schatz, A. H., Rayleigh-Ritz-Galerkin methods for Dirichlet’s Problem using subspaces without boundary conditions, Comm. Pure Appl. Math., 23, 653-675 (1970) · Zbl 0204.11102
[4] Falk, R. S., Approximate Solutions of some Variational Inequalities with Order of Convergence Estimates, (Ph.D. thesis (1971), Cornell University)
[5] Lions, J. L., Contrôle Optimal de Systèmes Gouvernés par des \($́\) Equations aux Dérivées Partielles (1968), Dunod: Dunod Paris · Zbl 0179.41801
[6] Morrey, C., Multiple Integrals in the Calculus of Variations (1966), Springer-Verlag: Springer-Verlag Berlin · Zbl 0142.38701
[7] Schechter, M., On \(L_p\) estimates and regularity, II, Math. Scand., 13, 47-69 (1963) · Zbl 0131.09505
[8] Stampacchia, G., Le problème de Dirichlet pour les équations elliptiques du second order à coéfficients discontinus, Ann. Inst. Fourier, 15, 189-258 (1965) · Zbl 0151.15401
[9] Strang, G., The finite element method and approximation theory, (Symposium on the Numerical Solution of Partial Differential Equations (May 1970), Univ. of Maryland) · Zbl 0179.22501
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