TY - JOUR
T1 - Recovery Type a Posteriori Error Estimates of Fully Discrete Finite Element Methods for General Convex Parabolic Optimal Control Problems
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 573
EP - 591
PY - 2012
DA - 2012/05
SN - 5
DO - http://doi.org/10.4208/nmtma.2012.m1117
UR - https://global-sci.org/intro/article_detail/nmtma/5950.html
KW - General convex optimal control problems, fully discrete finite element approximation,
a posteriori error estimates, superconvergence, recovery operator.
AB - <p style="text-align: justify;">This paper is concerned with recovery type a posteriori error estimates of fully discrete finite element approximation for general convex parabolic optimal control problems with pointwise control constraints. The time discretization is based on the backward Euler method. The state and the adjoint state are approximated by piecewise linear functions and the control is approximated by piecewise constant functions. We derive the superconvergence properties of finite element solutions. By using the superconvergence results, we obtain recovery type a posteriori error estimates. Some numerical examples are presented to verify the theoretical results.</p>