TY - JOUR T1 - A Posteriori Error Estimates of Semidiscrete Mixed Finite Element Methods for Parabolic Optimal Control Problems JO - East Asian Journal on Applied Mathematics VL - 1 SP - 85 EP - 108 PY - 2018 DA - 2018/02 SN - 5 DO - http://doi.org/10.4208/eajam.010314.110115a UR - https://global-sci.org/intro/article_detail/eajam/10781.html KW - A posteriori error estimates, optimal control problems, parabolic equations, elliptic reconstruction, semidiscrete mixed finite element methods. AB -

A posteriori error estimates of semidiscrete mixed finite element methods for quadratic optimal control problems involving linear parabolic equations are developed. The state and co-state are discretised by Raviart-Thomas mixed finite element spaces of order $k$, and the control is approximated by piecewise polynomials of order $k$ ($k≥0$). We derive our a posteriori error estimates for the state and the control approximations via a mixed elliptic reconstruction method. These estimates seem to be unavailable elsewhere in the literature, although they represent an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem.