A Goal-Oriented Adaptive Moreau-Yosida Algorithm for Control- and State-Constrained Elliptic Control Problems

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.

Author Details

Andreas Günther

Moulay Hicham Tber