References
- Murray , JD . 2003 . “ Mathematical biology: II. Spatial models and biomedical applications ” . In Interdisciplinary Applied Mathematics , 3rd , Vol. 18 , New York : Springer-Verlag .
- Bangerth , W and Rannacher , R . 2003 . Adaptive Finite Element Methods for Differential Equations, Lectures in Mathematics ETH Zürich , Basel : Birkhäuser Verlag .
- 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 ( 1 ) : 113 – 132 . (electronic)
- Becker , R , Kapp , H and Rannacher , R . 2000 . “ Adaptive finite element methods for optimization problems ” . In Numerical Analysis 1999 (Dundee), Chapman & Hall/CRC Research Notes Mathematics , Edited by: Griffiths , DF and Watson , GA . Vol. 420 , 21 – 42 . Boca Raton , , FL : Chapman & Hall/CRC .
- Arada , N , Casas , E and Tröltzsch , F . 2002 . Error estimates for the numerical approximation of a semilinear elliptic control problem . Comput. Optim. Appl. , 23 ( 2 ) : 201 – 229 .
- Deckelnick , K and Hinze , M . 2007 . Convergence of a finite element approximation to a stateconstrained elliptic control problem . SIAM J. Numer. Anal. , 45 ( 5 ) : 1937 – 1953 . (electronic)
- Marchuk , GI , Agoshkov , VI and Shutyaev , VP . 1996 . Adjoint Equations and Perturbation Algorithms in Nonlinear Problems , Boca Raton , , FL : CRC Press .
- Bors , D and Walczak , S . 2004 . Stability of Nonlinear Elliptic Systems with Distributed Parameters and Variable Boundary Data , Vol. 164/165 , Katholieke Universiteit Leuven, Belgium : Proceedings of the 10th International Congress on Computational and Applied Mathematics (ICCAM-2002) . pp. 117–130
- Eriksson , K , Estep , D , Hansbo , P and Johnson , C . 1995 . “ Introduction to adaptive methods for differential equations ” . In Acta Numerica, 1995 , Edited by: Iserles , I . 105 – 158 . Cambridge : Cambridge University Press .
- Estep , DJ , Larson , MG and Williams , RD . 2000 . Estimating the error of numerical solutions of systems of reaction-diffusion equations . Mem. Am. Math. Soc. , 146 ( 696 ) : viii+109
- Estep , D , Holst , M and Larson , M . 2005 . Generalized Green's functions and the effective domain of influence . SIAM J. Sci. Comput. , 26 ( 4 ) : 1314 – 1339 . (electronic)
- Chong , EKP and Zak , SH . 2001 . An Introduction to Optimization , 2nd , New York, NY, U.S.A. : Wiley .
- Bertsekas , DP . 2003 . Nonlinear programming , 2nd , Belmont, Mass, U.S.A. : Athena Scientific .
- Bertsekas , DP and Tsitsiklis , JN . 2000 . Gradient convergence in gradient methods with errors . SIAM J. Optim. , 10 ( 3 ) : 627 – 642 . (electronic)
- Wang , CY and Li , MX . 2005 . Convergence property of the Fletcher-Reeves conjugate gradient method with errors . J. Ind. Manag. Optim. , 1 ( 2 ) : 193 – 200 .
- Becker , R and Rannacher , R . 2001 . An optimal control approach to a posteriori error estimation in finite element methods . Acta Numer. , 10 : 1 – 102 .