Error estimates of mixed finite element methods for quadratic optimal control problems

Authors:
Xiaoqing Xing;Yanping Chen;Nianyu Yi
Affiliations:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, PR China;School of Mathematical Sciences, South China Normal University, Guangzhou 510631, PR China;Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

In this paper, we investigate the error estimates for the solutions of optimal control problems by mixed finite element methods. The state and costate are approximated by Raviart-Thomas mixed finite element spaces of order k and the control is approximated by piecewise polynomials of order k. Under the special constraint set, we will show that the control variable can be smooth in the whole domain. We derive error estimates of optimal order both for the state variables and the control variable.