Finite Element Approximation of Elliptic Dirichlet Optimal Control Problems

REFERENCES

• N. Arada , E. Casas , and F. Tröltzsch ( 2002 ). Error estimates for the numerical approximation of a semilinear elliptic control problem . Comput. Optim. Appl. 23 ( 2 ): 201 – 229 .
   Web of Science ®Google Scholar
• R. Becker . ( 2001 ). Adaptive Finite Elements for Optimal Control Problems . Habilitations-schrift, Institut für Angewandte Mathematik, Universität Heidelberg .
   Google Scholar
• R. Becker ( 2002 ). Mesh adaptation for Dirichlet flow control via nitsche's method . Comm. Numer. Methods Eng. 18 ( 9 ): 669 – 680 .
   Web of Science ®Google Scholar
• R. Becker , D. Meidner , and B. Vexler ( 2007 ). Efficient numerical solution of parabolic optimization problems by finite element methods . To appear in Optim. Methods Software .
   Google Scholar
• S. Brenner and R.L. Scott ( 1994 ). The Mathematical Theory of Finite Element Methods . Springer , Berlin, Heidelberg, New York .
   Google Scholar
• E. Casas and J.-P. Raymond ( 2006 ). Error estimates for the numerical approximation of Dirichlet boundary control for semilinear elliptic equations . SIAM J. Control Optim. 45 ( 5 ): 1586 – 1611 .
   Web of Science ®Google Scholar
• Ph. Clément ( 1975 ). Approximation by finite element functions using local regularization . Revue Franc. Automat. Inform. Rech. Operat. 9 ( 2 ): 77 – 84 .
   Google Scholar
• A.V. Fursikov ( 1999 ). Optimal Control of Distributed Systems: Theory and Applications . Volume 187 of Transl. Math. Monogr. AMS , Providence , RI .
   Google Scholar
• A.V. Fursikov , M.D. Gunzburger , and L.S. Hou ( 1998 ). Boundary value problems and optimal boundary control for the Navier–Stokes system: the two-dimensional case . SIAM J. Control Optim. 36 ( 3 ): 852 – 894 .
   Web of Science ®Google Scholar
• P. Grisvard ( 1992 ). Singularities in Boundary Value Problems . Springer-Verlag , Masson, Paris, Berlin .
   Google Scholar
• M.D. Gunzburger , L.S. Hou , and T. Svobodny ( 1991 ). Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with Dirichlet controls . Math. Model. Numer. Anal. 25 ( 6 ): 711 – 748 .
   Google Scholar
• M. Hinze ( 2004 ). A variational discretization concept in control constrained optimization: the linear-quadratic case . Comput. Optim. Appl. 30 ( 1 ): 45 – 61 .
   Web of Science ®Google Scholar
• M. Hinze and K. Kunisch ( 2004 ). Second order methods for boundary control of the instationary Navier-Stokes system . ZAMM Z. Angew. Math. Mech. 84 ( 3 ): 171 – 187 .
   Web of Science ®Google Scholar
• C. Johnson (1987). Numerical Solution of Partial Differential Equations by Finite Element Method . Cambridge University Press , Cambridge.
   Google Scholar
• H.-C. Lee and S. Kim ( 2004 ). Finite element approximation and computations of optimal dirichlet boundary control problems for the Boussinesq equations . J. Korean Math. Soc. 41 ( 4 ): 681 – 715 .
   Web of Science ®Google Scholar
• J.-L. Lions ( 1971 ). Optimal Control of Systems Governed by Partial Differential Equations . Volume 170 of Grundlehren Math. Wiss. Springer-Verlag , Berlin .
   Google Scholar
• C. Meyer and A. Rösch ( 2004 ). Superconvergence properties of optimal control problems . SIAM J. Control Optim. 43 : 970 – 985 .
   Web of Science ®Google Scholar
• R. Rannacher and B. Vexler ( 2005 ). A priori error estimates for the finite element discretization of elliptic parameter identification problems with pointwise measurements . SIAM J. Control Optim. 44 ( 5 ): 1844 – 1863 .
   Web of Science ®Google Scholar
• F. Tröltzsch ( 2005 ). Optimale Steuerung partieller Differentialgleichungen . Friedr. Vieweg & Sohn Verlag , Wiesbaden .
   Google Scholar