A priori error estimates for elliptic optimal control problems with a bilinear state equation
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
LP Modelling for the Time Optimal Control Problem of the Heat Equation
Journal of Mathematical Modelling and Algorithms
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Computational Optimization and Applications
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In this paper we develop a priori error analysis for Galerkin finite element discretizations of optimal control problems governed by linear parabolic equations. The space discretization of the state variable is done using usual conforming finite elements, whereas the time discretization is based on discontinuous Galerkin methods. For different types of control discretizations we provide error estimates of optimal order with respect to both space and time discretization parameters. The paper is divided into two parts. In the first part we develop some stability and error estimates for space-time discretization of the state equation and provide error estimates for optimal control problems without control constraints. In the second part of the paper, the techniques and results of the first part are used to develop a priori error analysis for optimal control problems with pointwise inequality constraints on the control variable.