Superconvergence properties of optimal control problems

SIAM Journal on Control and Optimization

Volumn 43, Issue 3, 2005, Pages 970-985

  Meyer, C ^a   Rosch A ^b  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^b JOHANN RADON INSTITUTE FOR COMPUTATIONAL AND APPLIED MATHEMATICS   (Austria)

Author keywords

Control constraints; Elliptic equations; Error estimates; Linear quadratic optimal control problems; Numerical approximation; Superconvergence

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; NUMERICAL ANALYSIS; PROBLEM SOLVING;

CONTROL CONSTRAINTS; ELLIPTIC EQUATIONS; ERROR ESTIMATES; LINEAR-QUADRATIC OPTIMAL CONTROL PROBLEMS; NUMERICAL APPROXIMATION; SUPERCONVERGENCE;

OPTIMAL CONTROL SYSTEMS;

EID: 19944424816     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012903431608     Document Type: Article

References (14)

1. N. ARADA, E. CASAS, AND F. TRÖLTZSCH, Error estimates for the numerical approximation of a semilinear elliptic control problem, Comput. Optim. Appl., 23 (2002), pp. 201-229.
2. F. BONNANS AND E. CASAS, An extension of Pontryagin's principle for state-constrained optimal control of semilinear elliptic equations and variational inequalities, SIAM J. Control Optim., 33 (1995), pp. 274-298.
3. D. BRAESS, Finite Elements, Springer-Verlag, Berlin, Heidelberg, 1992.
4. E. CASAS, M. MATEOS, AND F. TRÖLTZSCH, Error estimates for the numerical approximation of boundary semilinear elliptic control problems, Comput. Optim. Appl., submitted.
5. E. CASAS AND F. TRÖLTZSCH, Error estimates for linear-quadratic elliptic control problems, in Analysis and Optimization of Differential Systems, V. Barbu et al., eds., Kluwer Academic Publishers, Boston, 2003, pp. 89-100.
6. P. CIARLET, Basic error estimates for elliptic problems, in Handbook of Numerical Analysis Vol. II, Handb. Numer. Anal. II, North-Holland, Amsterdam, 1991, pp. 17-352.
7. R. FALK, Approximation of a class of optimal control problems with order of convergence estimates, J. Math. Anal. Appl., 44 (1973), pp. 28-47.
8. T. GEVECI, On the approximation of the solution of an optimal control problem governed by an elliptic equation, RAIRO Anal. Numér., 13 (1979), pp. 313-328.
9. P. GRISVARD, Elliptic Problems in Nonsmooth Domains, Pitman, Boston, 1985.
10. M. HINZE, A Generalized Discretization Concept for Optimal Control Problems with Control Constraints, Tech. rep. MATH-NM-02-2003, Technische Universität Dresden, Dresden, Germany, 2003.
11. K. KUNISCH AND A. RÖSCH, Primal-dual active set strategy for a general class of constrained optimal control problems, SIAM J. Optim., 13 (2002), pp. 321-334.
12. K. MALANOWSKI, Convergence of approximations vs. regularity of solutions for convex, control-constrained optimal control problems, Appl. Math. Optim., 8 (1981), pp. 69-95.
13. P. RAVIART AND J. THOMAS, Introduction à l' Analyse Numérique des Equations aux Dérivées Partielles, Masson, Paris, 1992.
14. A. RÖSCH, Error estimates for linear-quadratic control problems with control constraints, Optim. Methods and Softw., submitted.