TY - JOUR T1 - Superconvergence of Rectangular Mixed Finite Element Methods for Constrained Optimal Control Problem AU - Chen , Yanping AU - Dai , Li AU - Lu , Zuliang JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 56 EP - 75 PY - 2010 DA - 2010/02 SN - 2 DO - http://doi.org/10.4208/aamm.09-m0931 UR - https://global-sci.org/intro/article_detail/aamm/201.html KW - Constrained optimal control problem, linear elliptic equation, mixed finite element methods, rectangular partition, superconvergence properties. AB -
We investigate the superconvergence properties of the constrained quadratic elliptic optimal control problem which is solved by using rectangular mixed finite element methods. We use the lowest order Raviart-Thomas mixed finite element spaces to approximate the state and co-state variables and use piecewise constant functions to approximate the control variable. We obtain the superconvergence of $\mathcal{O}(h^{1+s})$ $(0$<$s\leq$<$1)$ for the control variable. Finally, we present two numerical examples to confirm our superconvergence results.