References
- Adjerid , S. 2006 . A posteriori error estimation for the method of lumped masses applied to second-order hyperbolic problems . Comput. Methods Appl. Mech. Engrg. , 195 : 4203 – 4219 .
- Ainsworth , M. and Oden , J. T. 2000 . “ A Posteriori Error Estimation in Finite Element Analysis ” . New York : Wiley Interscience .
- Becker , R. , Kapp , H. and Rannacher , R. 2000 . Adaptive finite element methods for optimal control of partial differential equations: Basic concept . SIAM J. Control Optim. , 39 : 113 – 132 .
- Ciarlet , P. G. 2002 . “ The Finite Element Method for Elliptic Problems ” . Philadelphia, PA : Society for Industrial and Applied Mathematics .
- Falk , F. S. 1973 . Approximation of a class of optimal control problems with order of convergence estimates . J. Math. Anal. Appl. , 44 : 28 – 47 .
- Fu , H. F. and Rui , H. X. 2009 . A priori error estimates for optimal control problems governed by transient advection-diffusion equations . J. Sci. Comput. , 38 : 290 – 315 .
- Geveci , T. 1979 . On the approximation of the solution of an optimal control problem governed by an elliptic equation . RAIRO Anal. Numer. , 13 : 313 – 328 .
- Gong , W. and Yan , N. N. 2009 . A posteriori error estimate for boundary control problems governed by the parabolic partial differential equations . J. Comput. Math. , 27 : 68 – 88 .
- Houston , P. and Süli , E. 2000 . Adaptive Lagrange-Galerkin methods for unsteady convection-diffusion problems . Math. Comp. , 70 : 77 – 106 .
- Kufner , A. , John , O. and Fucik , S. 1977 . “ Function Spaces ” . Leyden, , The Netherlands : Nordhoff .
- Lai , J. , Huang , J. G. and Shi , Z. C. 2010 . A lumped mass finite element method for vibration analysis of elastic plate-plate structures . Sci. China Math. , 53 : 1453 – 1474 .
- R. Li and W.B. Liu, http://circus.math.pku.edu.cn/AFEPack
- Li , R. , Liu , W. B. , Ma , H. P. and Tang , T. 2002 . Adaptive finite elememt approximation of elliptic optimal control . SIAM J. Control Optim. , 41 : 1321 – 1349 .
- Lions , J. L. 1971 . “ Optimal Control of Systems Governed by Partial Differential Equations ” . Berlin : Springer-Verlag .
- Liu , W. B. and Tiba , D. 2001 . Error estimates for the finite element approximation of nonlinear optimal control problems . J. Numer. Funct. Optim. , 22 : 953 – 972 .
- Liu , W. B. and Yan , N. N. 2001 . A posteriori error estimates for distributed convex optimal control problems . Adv. Comput. Math. , 15 : 285 – 309 .
- Liu , W. B. and Yan , N. N. 2002 . A posteriori error estimates for control problems governed by stokes equations . SIAM J. Numer. Anal. , 40 : 1850 – 1869 .
- Liu , W. B. and Yan , N. N. 2003 . A posteriori error estimates for optimal control problems governed by parabolic equations . Numer. Math. , 93 : 497 – 521 .
- Meidner , D. and Vexler , B. 2008 . A priori error estimates for space-time finite element discretization of parabolic optimal control problems. Part I: Problems without control constraints . SIAM J. Control Optim. , 47 : 1150 – 1177 .
- Meidner , D. and Vexler , B. 2008 . A priori error estimates for space-time finite element discretization of parabolic optimal control problems. Part II: problems with control constraints . SIAM J. Control Optim. , 47 : 1301 – 1329 .
- Neittaanmaki , P. and Tiba , D. 1994 . “ Optimal Control of Nonlinear Parabolic Systems. Theorey, Algorithms and Applications ” . New York : M. Dekker .
- Pironneau , O. 1984 . “ Optimal Shape Design for Elliptic Systems ” . Berlin : Springer-Verlag .
- Rösch , A. 2005 . Error estimates for linear-quadrature control problems with control constraints . Optim. Methods Softw. , 21 : 121 – 134 .
- Saito , N. 2004 . A holomorphic semigroup approach to the lumped mass finite element method . J. Comput. Appl. Math. , 169 : 71 – 85 .
- Thomée , V. 1997 . “ Galerkin Finite Element Methods for Parabolic Problems ” . Berlin : Springer Series in Computational Mathematics, Springer-Verlag .
- Tiba , D. 1995 . “ Lectures on the Optimal Control of Elliptic Equations ” . Finland : University of Jyvaskyla Press .
- Verfürth , R. 1996 . “ A Review of Posteriori Error Estimation and Adaptive Mesh Refinement Techniques ” . New York : Wiley-Teubner .