TY - JOUR
T1 - A Goal-Oriented Adaptive Moreau-Yosida Algorithm for Control- and State-Constrained Elliptic Control Problems
AU - Günther , Andreas
AU - Tber , Moulay Hicham
JO - Advances in Applied Mathematics and Mechanics
VL - 3
SP - 426
EP - 448
PY - 2018
DA - 2018/05
SN - 8
DO - http://doi.org/10.4208/aamm.2014.m663
UR - https://global-sci.org/intro/article_detail/aamm/12096.html
KW - Elliptic optimal control problem, control and state constraints, Moreau-Yosida regularization, semi-smooth Newton method, variational discretization, goal-oriented adaptivity.
AB - <p style="text-align: justify;">In this work, we develop an adaptive algorithm for solving elliptic optimal
control problems with simultaneously appearing state and control constraints. The
algorithm combines a Moreau-Yosida technique for handling state constraints with a
semi-smooth Newton method for solving the optimality systems of the regularized
sub-problems. The state and adjoint variables are discretized using continuous piecewise
linear finite elements while a variational discretization concept is applied for the
control. To perform the adaptive mesh refinements cycle we derive local error estimators
which extend the goal-oriented error approach to our setting. The performance of
the overall adaptive solver is assessed by numerical examples.</p>