A Goal-Oriented Adaptive Moreau-Yosida Algorithm for Control- and State-Constrained Elliptic Control Problems
2016 ◽
Vol 8
(3)
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pp. 426-448
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Keyword(s):
AbstractIn 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.
2008 ◽
Vol 46
(3)
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pp. 487-510
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2006 ◽
Vol 26
(1-3)
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pp. 137-153
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2006 ◽
Vol 43
(6)
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pp. 2517-2543
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Keyword(s):
2014 ◽
Vol 68
(8)
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pp. 789-803
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2010 ◽
Vol 52
(1)
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pp. 181-207
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2014 ◽
Vol 32
(5_6)
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pp. 707-719