[1]    A. Azzam and E. Kreyszig, On solutions of elliptic equations satisfying mixed boundary conditions, SIAM J. Math. Anal. 13 (1982), 254-262.

[2]    M. Bergounioux, Optimal control of an obstacle problem, Appl. Math. Optim. 36 (1997), 147-172.

[3]    S. Beuchler, C. Pechstein and D. Wachsmuth, Boundary concentrated finite elements for optimal boundary control problems of elliptic PDEs, Comput. Optim. Appl. 51 (2012), 883-908.

[4]    S. Brenner and L. R. Scott, The Mathematical Theory of Finite Element Methods, Springer, New York, 2008.

[5]    E. Casas and M. Mateos, Uniform convergence of the FEM. Applications to state constrained control problems, Comput. Appl. Math. 21 (2002), 67-100.

[6]    E. Casas and M. Mateos, Error estimates for the numerical approximation of Neumann control problems, Comput. Optim. Appl. 39 (2008), 265-295.

[7]    E. Casas and M. Mateos, Dirichlet control problems in smooth and nonsmooth convex plain domains, Control Cybernetics 40 (2011), 931-955.

[8]    E. Casas, M. Mateos and F. Tröltzsch, Error estimates for the numerical approximation of boundary semilinear elliptic control problems, Comput. Optim. Appl. 31 (2005), 193-219.

[9]    E. Casas and J. P. Raymond, Error estimates for the numerical approximation of Dirichlet boundary control for semilinear elliptic equations, SIAM J. Control Optim. 45 (2006), 1586-1611.

[10]    P. G. Ciarlet, The Finite Element Method for Elliptic Problems, SIAM, Philadelphia, 2002.

[11]    K. Deckelnick, A. Günther and M. Hinze, Finite element approximation of elliptic control problems with constraints on the gradient, Numer. Math. 111 (2009), 335-350.

[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.

[13]    P. Gamallo, E. Hernández and A. Peters, On the error estimates for the finite element approximation of a class of boundary optimal control systems, Numer. Funct. Anal. Optim. 32 (2011), 383-396.

[14]    C. M. Gariboldi and D. A. Tarzia, Convergence of distributed optimal controls on the internal energy in mixed elliptic problems when the heat transfer coefficient goes to infinity, Appl. Math. Optim. 47 (2003), 213-230.

[15]    C. M. Gariboldi and D. A. Tarzia, Convergence of boundary optimal control problems with restrictions in mixed elliptic Stefan-like problems, Advances in Differential Equations and Control Processes 1 (2008), 113-132.

[16]    R. Haller-Dintelmann, C. Meyer, J. Rehberg and A. Schiela, Hölder continuity and optimal control for nonsmooth elliptic problems, Appl. Math. Optim. 60 (2009), 397-428.

[17]    M. Hintermüller and M. Hinze, Moreau-Yosida regularization in state constrained elliptic control problems: error estimates and parameter adjustment, SIAM J. Numer. Anal. 47 (2009), 1666-1683.

[18]    M. Hinze, A variational discretization concept in control constrained optimization: the linear-quadratic case, Comput. Optim. Appl. 30 (2005), 45-61.

[19]    M. Hinze, Discrete concepts in PDE constrained optimization, Optimization with PDE Constrained, M. Hinze, R. Pinnau, R. Ulbrich and S. Ulbrich, eds., Chapter 3, Springer, New York, 2009.

[20]    M. Hinze and U. Matthes, A note on variational dicretization of elliptic Neumann boundary control, Control Cybernetics 38 (2009), 577-591.

[21]    D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and their Applications, SIAM, Philadelphia, 2000.

[22]    L. Lanzani, L. Capogna and R. M. Brown, The mixed problem in  for some two-dimensional Lipschitz domain, Math. Ann. 342 (2008), 91-124.

[23]    J. L. Lions, Contrôle optimal des systèmes gouvernés par des équations aux dérivées partielles, Dunod, Paris, 1968.

[24]    E. B. Mermri and W. Han, Numerical approximation of a unilateral obstacle problem, J. Optim. Theory Appl. 153 (2012), 177-194.

[25]    E. Shamir, Regularization of mixed second order elliptic problems, Israel J. Math. 6 (1968), 150-168.

[26]    E. D. Tabacman and D. A. Tarzia, Sufficient and/or necessary condition for the heat transfer coefficient on  and the heat flux on  to obtain a steady-state two-phase Stefan problem, J. Differential Equations 77 (1989), 16-37.

[27]    D. A. Tarzia, An inequality for the constant heat flux to obtain a steady-state   two-phase Stefan problem, Eng. Anal. 5 (1988), 177-181.

[28]    D. A. Tarzia, Numerical analysis for the heat flux in a mixed elliptic problem to obtain a discrete steady-state two-phase Stefan problem, SIAM J. Numer. Anal. 33 (1996), 1257-1265.

[29]    D. A. Tarzia, Numerical analysis of a mixed elliptic problem with flux and convective boundary conditions to obtain a discrete solution of non-constant sign, Numer. Methods Partial Differential Equations 5 (1999), 355-369.

[30]    F. Tröltzsch, Optimal control of partial differential equations, Theory, Methods and Applications, American Mathematical Society, Providence, 2010.

[31]    M. Yan, L. Chang and N. Yan, Finite element method for constrained optimal control problems governed by nonlinear elliptic PDEs, Math. Control Related Fields 2 (2012), 183-194.

[32]    Y. Ye, C. K. Chan and H. W. J. Lee, The existence results for obstacle optimal control problems, Appl. Math. Comput. 214 (2009), 451-456.