Hongfei Fu^{1}, Hongxing Rui^{2}, Hui Guo^{1}
[1] D. ParraGuevara and Y.N. Skiba, Elements of the mathematical modelling in the control of pollutants emissions, Ecol. Model., 167 (2003), 263275. [2] J. Zhu and Q. Zeng, A mathematical formulation for optimal control of air pollution, Sci. China Ser. D, 46 (2003), 9941002. [3] S. Collis and M. Heinkenschloss, Analysis of the streamline upwind/Petrov Galerkin method applied to the solution of optimal control problems, CAAM TR0201, 2002. [4] M. Heinkenschloss and D. Leykekhman, Local error estimates for SUPG solutions of advectiondominated elliptic linearquadratic optimal control problems, SIAM J. Numer. Anal., 47 (2010), 46074638. [5] R. Becker and B. Vexler, Optimal control of the convectiondiffusion equation using stabilized finite element methods, Numer. Math., 106 (2007), 349367. [6] M. Braack, Optimal control in fluid mechanics by finite elements with symmetric stabilization, SIAM J. Control Optim., 48 (2009), 672687. [7] N. Yan and Z. Zhou, A priori and a posteriori error analysis of edge stabilization Galerkin method for the optimal control problem governed by convectiondominated diffusion equation, J. Comput. Appl. Math., 223 (2009), 198217. [8] N. Yan and Z. Zhou, A RT mixed FEM/DG scheme for optimal control governed by convection diffusion equations, J. Sci. Comput., 41 (2009), 273299. [9] R.A. Bartlett, M. Heinkenschloss, D. Ridzal and B. G. Waanders, Domain decomposition methods for advection dominated linearquadratic elliptic optimal control problems, Comput. Methods Appl. Mech. Engrg., 195 (2006), 64286447. [10] H. Fu and H. Rui, A priori error estimates for optimal control problems governed by transient advectiondiffusion equations, J. Sci. Comput., 38 (2009), 290315. [11] Z. Zhou and N. Yan, The local discontinuous Galerkin method for optimal control problem governed by convection diffusion equations, Int. J. Numer. Anal. Model., 7 (2010), 681699. [12] H. Fu, A characteristic finite element method for optimal control problems governed by convectiondiffusion equations, J. Comput. Appl. Math., 235 (2010), 825836. [13] H. Fu and H. Rui, A characteristicmixed finite element method for timedependent convectiondiffusion optimal control problem, Appl. Math. Comput., 218 (2011), 34303440. [14] S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods, SpringerVerlag, 2002. [15] J.L. Lions, Optimal Control of Systems Governed by Partial Differential Equations, SpringerVerlag, Berlin, 1971. [16] O. Pironneau, Optimal Shape Design for Elliptic Systems, SpringerVerlag, Berlin, 1984. [17] D. Tiba, Lectures on the Optimal Control of Elliptic Equations, University of Jyvaskyla Press, Finland, 1995. [18] J.L. Lions and E. Magenes, Non homogeneous boundary value problems and applications, SpringerVerlag, Berlin, 1972. [19] J. Douglas and T.F. Russell, Numerical methods for convectiondominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures, SIAM J. Numer. Anal., 19 (1982), 871885. [20] H. Rui and M. Tabata, A second order characteristic finite element scheme for convectiondiffusion problems, Numer. Math., 92 (2002), 161177. [21] R. Dautray and J.L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, Vol. 5, SpringerVerlag, Berlin, 1992. [22] C. Meyer and A. Rösch, Superconvergence properties of optimal control problems, SIAM J. Control Optim., 43 (2004), 970985. [23] E. Süli, Convergence and nonlinear stability of the LagrangeGalerkin method for the Navier Stokes equations, Numer. Math., 53 (1988), pp. 459483. [24] F.S. Falk, Approximation of a class of optimal control problems with order of convergence estimates, J. Math. Anal. Appl., 44 (1973), 2847. [25] X. Xing and Y. Chen, Error estimates of mixed methods for optimal control problems governed by parabolic equations, Int. J. Numer. Meth. Engng., 75 (2008), 735754. [26] V. Thom′ee, Galerkin finite element methods for parabolic problems, Springer Series in Computational Mathematics, SpringerVerlag, Berlin, 2006. 
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