EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 20 / No 3 (July-September 2014) ESAIM: COCV, 20 3 (2014) 803-822 References
Free Access
Issue
ESAIM: COCV
Volume 20, Number 3, July-September 2014
Page(s) 803 - 822
DOI https://doi.org/10.1051/cocv/2013084
Published online 05 June 2014
  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) 201–229. [CrossRef] [MathSciNet] [Google Scholar]
  2. M. Bergounioux and K. Kunisch, Primal-dual strategy for state-constrained optimal control problems. Comput. Optim. Appl. 22 (2002) 193–224. [CrossRef] [MathSciNet] [Google Scholar]
  3. M. Bergounioux and K. Kunisch, On the structure of Lagrange multipliers for state-constrained optimal control problems. Systems Control Lett. 48 (2003) 169–176. Optimization and control of distributed systems. [CrossRef] [MathSciNet] [Google Scholar]
  4. H. Blum and R. Rannacher, On the boundary value problem of the biharmonic operator on domains with angular corners. Math. Methods Appl. Sci. 2 (1980) 556–581. [CrossRef] [MathSciNet] [Google Scholar]
  5. S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods. Springer-Verlag, New York, Berlin, Heidelberg (1994). [Google Scholar]
  6. E. Casas, Control of an elliptic problem with pointwise state constraints. SIAM J. Control Optim. 24 (1986) 1309–1318. [CrossRef] [MathSciNet] [Google Scholar]
  7. E. Casas, J.C. de los Reyes and F. Tröltzsch, Sufficient second order optimality conditions for semilinear control problems with pointwise state constraints. SIAM J. Optim. 19 (2008) 616–643. [CrossRef] [MathSciNet] [Google Scholar]
  8. E. Casas and M. Mateos, Uniform convergence of the FEM. Applications to state constrained control problems. Comput. Appl. Math. 21 (2002) 67–100. [MathSciNet] [Google Scholar]
  9. E. Casas, Error estimates for the numerical approximation of semilinear elliptic control problems with finitely many state contraints. ESAIM: COCV 8 (2002) 345–374. [CrossRef] [EDP Sciences] [Google Scholar]
  10. E. Casas and M. Mateos, Numerical approximation of elliptic control problems with finitely many pointwise constraints. Comput. Optim. Appl. 51 (2012) 1319–1343. [CrossRef] [MathSciNet] [Google Scholar]
  11. E. Casas and F. Tröltzsch, Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems. ESAIM: COCV 16 (2010) 581–600. [CrossRef] [EDP Sciences] [Google Scholar]
  12. S. Cherednichenko, K. Krumbiegel and A. Rösch, Error estimates for the Lavrentiev regularization of elliptic optimal control problems. Inverse Problems 24 (2008) 21. [CrossRef] [Google Scholar]
  13. P.G. Ciarlet, Basic error estimates for elliptic problems, in Handbook of numerical analysis, Vol. II, Handb. Numer. Anal., II. North-Holland, Amsterdam (1991) 17–351 [Google Scholar]
  14. G. Dal Maso, F. Murat, L. Orsina and A. Prignet, Renormalized solutions of elliptic equations with general measure data. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 28 (1999) 741–808. [MathSciNet] [Google Scholar]
  15. K. Deckelnick and M. Hinze, Convergence of a finite element approximation to a state constrained elliptic control problem. SIAM J. Numer. Anal. 35 (2007) 1937–1953. [CrossRef] [MathSciNet] [Google Scholar]
  16. K. Deckelnick and M. Hinze, Numerical analysis of a control and state constrained elliptic control problem with piecewise constant control approximations, in Proc. of ENUMATH, 2007. Numer. Math. Advanced Appl., edited by K. Kunisch, G. Of and O. Steinbach. Springer, Berlin (2008) 597–604. [Google Scholar]
  17. M. Degiovanni and M. Scaglia, A variational approach to semilinear elliptic equations with measure data. Discrete Contin. Dyn. Syst. 31 (2011) 1233–1248. [CrossRef] [MathSciNet] [Google Scholar]
  18. D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order. Classics in Math. Reprint of the 1998 edition. Springer-Verlag, Berlin (2001). [Google Scholar]
  19. W. Gong and N. Yan, A mixed finite element scheme for optimal control problems with pointwise state constraints. J. Sci. Comput. 46 (2011) 182–203. [CrossRef] [MathSciNet] [Google Scholar]
  20. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman, Boston-London-Melbourne, 1985. [Google Scholar]
  21. M. Hinze, R. Pinnau, M. Ulbrich and S. Ulbrich, Optimization with PDE constraints, vol. 23. Math. Model.: Theory Appl. Springer, New York (2009). [Google Scholar]
  22. D. Leykekhman, D. Meidner and B. Vexler, Optimal error estimates for finite element discretization of elliptic optimal control problems with finitely many pointwise state constraints. Comput. Optim. Appl. 55 (2013) 769–802. [Google Scholar]
  23. W. Liu, W. Gong and N. Yan, A new finite element approximation of a state-constrained optimal control problem. J. Comput. Math. 27 (2009) 97–114. [MathSciNet] [Google Scholar]
  24. C. Meyer, Error estimates for the finite-element approximation of an elliptic control problem with pointwise state and control constraints. Control Cybernet 37 (2008) 51–83. [Google Scholar]
  25. C. Meyer, U. Prüfert and Tröltzsch, On two numerical methods for state-constrained elliptic control problems. Optim. Methods Softw. 22 (2007) 871–899. [Google Scholar]
  26. C. Meyer, Error estimates for the finite-element approximation of an elliptic control problem with pointwise state and control constraints. Control and Cybernetics 37 (2008) 51–85. [MathSciNet] [Google Scholar]
  27. K. Pieper and B. Vexler, A priori error analysis for discretization of sparse elliptic optimal control problems in measure space. SIAM J. Control Optim. 51 (2013) 2788–2808. [CrossRef] [MathSciNet] [Google Scholar]
  28. A. Rösch and S. Steinig, A priori error estimates for a state-constrained elliptic optimal control problem. ESAIM: M2AN 46 (2012) 1107–1120. [CrossRef] [EDP Sciences] [Google Scholar]
  29. W. Rudin, Real and Complex Analysis. McGraw-Hill, London (1970). [Google Scholar]
  30. A.H. Schatz and L.B. Wahlbin, Interior maximum norm estimates for finite element methods. Math. Comput. 31 (1977) 414–442. [CrossRef] [Google Scholar]
  31. G. Stampacchia, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus. Ann. Inst. Fourier, Grenoble 15 (1965) 189–258. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.