Free access
Issue
ESAIM: COCV
Volume 17, Number 3, July-September 2011
Page(s) 771 - 800
DOI http://dx.doi.org/10.1051/cocv/2010025
Published online 06 August 2010
  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]
  2. S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods. Springer-Verlag, New York-Berlin-Heidelberg (1984).
  3. E. Casas and V. Dhamo, Error estimates for the numerical approximation of a quasilinear Neumann problem under minimal regularity of the data. (Submitted).
  4. E. Casas and M. Mateos, Uniform convergence of the FEM. Applications to state constrained control problems. Comp. Appl. Math. 21 (2007) 67–100.
  5. E. Casas and F. Tröltzsch, Optimality conditions for a class of optimal control problems with quasilinear elliptic equations. SIAM J. Control Optim. 48 (2009) 688–718. [CrossRef] [MathSciNet]
  6. P. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1978).
  7. J. Douglas, Jr. and T. Dupont, A Galerkin method for a nonlinear Dirichlet problem. Math. Comp. 29 (1975) 689–696. [CrossRef] [MathSciNet]
  8. M. Hinze, A variational discretization concept in control constrained optimization: The linear-quadratic case. Comput. Optim. Appl. 30 (2005) 45–61. [CrossRef] [MathSciNet]
  9. I. Hlaváček, Reliable solution of a quasilinear nonpotential elliptic problem of a nonmonotone type with respect to the uncertainty in coefficients. J. Math. Anal. Appl. 212 (1997) 452–466. [CrossRef] [MathSciNet]
  10. I. Hlaváček, M. Křížek and J. Malý, On Galerkin approximations of quasilinear nonpotential elliptic problem of a nonmonotone type. J. Math. Anal. Appl. 184 (1994) 168–189. [CrossRef] [MathSciNet]
  11. L. Liu, M. Křížek and P. Neittaanmäki, Higher order finite element approximation of a quasilinear elliptic boundary value problem of a non-monotone type. Appl. Math. 41 (1996) 467–478. [MathSciNet]
  12. R. Rannacher and R. Scott, Some optimal error estimates for piecewise finite element approximations. Math. Comp. 38 (1982) 437–445. [CrossRef] [MathSciNet]
  13. P. Raviart and J. Thomas, Introduction à l'Analyse Numérique des Équations aux Dérivées Partielles. Masson, Paris (1983).