A Goal-Oriented Adaptive Moreau-Yosida Algorithm for Control- and State-Constrained Elliptic Control Problems
Year: 2016
Author: Andreas Günther, Moulay Hicham Tber
Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 3 : pp. 426–448
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2014.m663
Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 3 : pp. 426–448
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Elliptic optimal control problem control and state constraints Moreau-Yosida regularization semi-smooth Newton method variational discretization goal-oriented adaptivity.