MIXED DISCONTINUOUS GALERKIN TIME-STEPPING METHOD FOR LINEAR PARABOLIC OPTIMAL CONTROL PROBLEMS
MIXED DISCONTINUOUS GALERKIN TIME-STEPPING METHOD FOR LINEAR PARABOLIC OPTIMAL CONTROL PROBLEMS作者机构：School of Mathematical Sciences South China Normal University Guangzhou 510631 China School of Mathematics and Statistics Beihua University Jilin 132013 China
出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)
年 卷 期：2015年第33卷第2期
页 面：158-178页
核心收录：
学科分类：0711[理学-系统科学] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 070102[理学-计算数学] 081101[工学-控制理论与控制工程] 071101[理学-系统理论] 0811[工学-控制科学与工程] 0701[理学-数学]
基 金：Acknowledgments. The authors would like to thank the editor and the anonymous referee for their valuable comments and suggestions on an earlier version of this paper. The work of T. Hou was supported by China Postdoctoral Science Foundation funded project (2013M542188). The work of Y. Chen was supported by National Science Foundation of China (91430104 11271145) and Specialized Research Fund for the Doctoral Program of Higher Education (20114407110009)
主 题：A priori error estimates A posteriori error estimates Mixed finite element,Discontinuous Galerkin method Parabolic control problems.
摘 要：In this paper, we discuss the mixed discontinuous Galerkin （DG） finite element ap- proximation to linear parabolic optimal control problems. For the state variables and the co-state variables, the discontinuous finite element method is used for the time dis- cretization and the Raviart-Thomas mixed finite element method is used for the space discretization. We do not discretize the space of admissible control but implicitly utilize the relation between co-state and control for the discretization of the control. We de- rive a priori error estimates for the lowest order mixed DG finite element approximation. Moveover, for the element of arbitrary order in space and time, we derive a posteriori L2（O, T; L2（Ω）） error estimates for the scalar functions, assuming that only the underlying mesh is static. Finally, we present an example to confirm the theoretical result on a priori error estimates.
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