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 - <p style="text-align: justify;">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.</p>