In this paper, we investigate a priori and a posteriori error estimates of fully discrete $H$1-Galerkin mixed finite element methods for parabolic optimal control problems. The state variables and co-state variables are approximated by the lowest order Raviart-Thomas mixed finite element and linear finite element, and the control variable is approximated by piecewise constant functions. The time discretization of the state and co-state are based on finite difference methods. First, we derive a priori error estimates for the control variable, the state variables and the adjoint state variables. Second, by use of energy approach, we derive a posteriori error estimates for optimal control problems, assuming that only the underlying mesh is static. A numerical example is presented to verify the theoretical results on a priori error estimates.
}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2019.m1623}, url = {https://global-sci.com/article/90388/fully-discrete-hsup1sup-galerkin-mixed-finite-element-methods-for-parabolic-optimal-control-problems} }