Free Access
Issue
ESAIM: M2AN
Volume 46, Number 5, September-October 2012
Page(s) 1107 - 1120
DOI https://doi.org/10.1051/m2an/2011076
Published online 13 February 2012
  1. R.A. Adams and J.J.F. Fournier, Sobolev spaces. Academic Press, San Diego (2007).
  2. S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solution of elliptic partial differential equations satisfying general boundary conditions I. Comm. Pure Appl. Math. 12 (1959) 623–727. [CrossRef] [MathSciNet]
  3. J.W. Barrett and C.M. Elliott, A finite-element method for solving elliptic equations with Neumann data on a curved boundary using unfitted meshes. IMA J. Numer. Anal. 4 (1984) 309–325. [CrossRef] [MathSciNet]
  4. J. Bergh and J. Löfström, Interpolation spaces. Springer, Berlin (1976).
  5. M. Bergounioux, K. Ito and K. Kunisch, Primal-dual strategy for constrained optimal control problems. SIAM J. Control Optim. 37 (1999) 1176–1194. [CrossRef] [MathSciNet]
  6. E. Casas, Control of an elliptic problem with pointwise state constraints. SIAM J. Control Optim. 4 (1986) 1309–1322. [CrossRef] [MathSciNet]
  7. 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]
  8. S. Cherednichenko and A. Rösch, Error estimates for the regularization of optimal control problems with pointwise control and state constraints. Z. Anal. Anwendungen 27 (2008) 195–212. [CrossRef]
  9. S. Cherednichenko, K. Krumbiegel and A. Rösch, Error estimates for the Lavrentiev regularization of elliptic optimal control problems. Inverse Problems 24 (2008).
  10. P.G. Ciarlet, The finite element method for elliptic problems. SIAM Classics In Applied Mathematics, Philadelphia (2002).
  11. J.C. de los Reyes, C. Meyer and B. Vexler, Finite element error analysis for state-constrained optimal control of the Stokes equations. Control and Cybernetics 37 (2008) 251–284. [MathSciNet]
  12. K. Deckelnick and M. Hinze, Convergence of a finite element approximation to a state constrained elliptic control problem. SIAM J. Numer. Anal. 45 (2007) 1937–1953. [CrossRef] [MathSciNet]
  13. K. Deckelnick and M. Hinze, Numerical analysis of a control and state constrained elliptic control problem with piecewise constant control approximations, in Numerical Mathematics and Advanced Applications, edited by K. Kunisch, G. Of and O. Steinbach, Berlin, Heidelberg, Springer-Verlag (2008) 597–604.
  14. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman, Boston (1985).
  15. M. Hintermüller, K. Ito and K. Kunisch, The primal-dual active set strategy as a semi-smooth Newton method. SIAM J. Optim. 13 (2003) 865–888. [CrossRef] [MathSciNet]
  16. M. Hinze, R. Pinnau, M. Ulbrich and S. Ulbrich, Optimization with PDE Constraints. Springer-Verlag, Berlin (2009).
  17. K. Kunisch and A. Rösch, Primal-dual active set strategy for a general class of constrained optimal control problems. SIAM J. Optim. 13 (2002) 321–334. [CrossRef] [MathSciNet]
  18. 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]
  19. C. Meyer, A. Rösch and F. Tröltzsch, Optimal control of PDEs with regularized pointwise state constraints. Comput. Optim. Appl. 33 (2006) 209–228. [CrossRef] [MathSciNet]
  20. P. Neittaanmaki, J. Sprekels and D. Tiba, Optimization of Elliptic Systems. Springer-Verlag, New York (2006).
  21. R. Rannacher, Zur L-Konvergenz linearer finiter elemente beim Dirichlet-problem. Math. Z. 149 (1976) 69–77. [CrossRef] [MathSciNet]
  22. A. Rösch and F. Tröltzsch, Existence of regular Lagrange multipliers for elliptic optimal control problem with pointwise control-state constraints. SIAM J. Optim. 45 (2006) 548–564. [CrossRef]
  23. A.H. Schatz, Pointwise error estimates and asymptotic error expansion inequalities for the finite element method on irregular grids. I : Global estimates. Math. Comput. 67 (1998) 877–899. [CrossRef]
  24. A.H. Schatz and L.B. Wahlbin, Interior maximum norm estimates for the finite element method. Math. Comput. 31 (1977) 414–442. [CrossRef]
  25. A.H. Schatz and L.B. Wahlbin, On the quasi-optimality in L of the Formula -projection into finite element spaces. Math. Comput. 38 (1982) 1–22.
  26. A. Schmidt and K.G. Siebert, Design of Adaptive Finite Element Software, The Finite Element Toolbox ALBERTA. Springer-Verlag, Berlin (2000).
  27. F. Tröltzsch, Regular Lagrange multipliers for problems with pointwise mixed control-state constraints. SIAM J. Optim. 15 (2005) 616–634. [CrossRef]
  28. F. Tröltzsch, Optimal control of partial differential equations. Amer. Math. Soc., Providence, Rhode Island (2010).
  29. D.Z. Zanger, The inhomogeneous Neumann problem in Lipschitz domains. Commun. Partial Differ. Equ. 25 (2000) 1771–1808.

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