A priori L2-discretization error estimates for the state in elliptic optimization problems with pointwise inequality state constraints
A priori L2-discretization error estimates for the state in elliptic optimization problems with pointwise inequality state constraints
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03.2016Publisher
Institut für Numerische Simulation (INS)Publisher Location
BonnMetadata
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https://hdl.handle.net/20.500.11811/11851
Abstract
In this paper, an elliptic optimization problem with pointwise inequality constraints on the state is considered. The main contribution of this paper are a priori L2-error estimates for the discretization error in the optimal states. Due to the non separability of the space for the Lagrange multipliers for the inequality constraints, the problem is tackled by separation of the discretization error into two components. First, the state constraints are discretized. Second, with discretized inequality constraints, a duality argument for the error due to the discretization of the PDE is employed. For the second stage an a priori error estimate is derived with constants depending on the regularity of the dual problem. Finally, we discuss two cases in which these constants can be bounded in a favorable way; leading to higher order estimates than those induced by the known L2-error in the control variable. More precisely, we consider a given fixed number of pointwise inequality constraints and a case of infinitely many but only weakly active constraints.
Classification (DDC)
510 Mathematik 518 Numerische AnalysisFirst Publication
https://ins.uni-bonn.de/publication/preprintsRelated Publications
https://doi.org/10.1007/s00211-017-0906-6Part of Series
INS Preprints ; 1606Neitzel, Ira; Wollner, Winnifried: A priori L2-discretization error estimates for the state in elliptic optimization problems with pointwise inequality state constraints. In: INS Preprints, 1606.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11851
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11851
@unpublished{handle:20.500.11811/11851,
author = {{Ira Neitzel} and {Winnifried Wollner}},
title = {A priori L2-discretization error estimates for the state in elliptic optimization problems with pointwise inequality state constraints},
publisher = {Institut für Numerische Simulation (INS)},
year = 2016,
month = mar,
INS Preprints},
volume = 1606,
note = {In this paper, an elliptic optimization problem with pointwise inequality constraints on the state is considered. The main contribution of this paper are a priori L2-error estimates for the discretization error in the optimal states. Due to the non separability of the space for the Lagrange multipliers for the inequality constraints, the problem is tackled by separation of the discretization error into two components. First, the state constraints are discretized. Second, with discretized inequality constraints, a duality argument for the error due to the discretization of the PDE is employed. For the second stage an a priori error estimate is derived with constants depending on the regularity of the dual problem. Finally, we discuss two cases in which these constants can be bounded in a favorable way; leading to higher order estimates than those induced by the known L2-error in the control variable. More precisely, we consider a given fixed number of pointwise inequality constraints and a case of infinitely many but only weakly active constraints.},
url = {https://hdl.handle.net/20.500.11811/11851}
}
author = {{Ira Neitzel} and {Winnifried Wollner}},
title = {A priori L2-discretization error estimates for the state in elliptic optimization problems with pointwise inequality state constraints},
publisher = {Institut für Numerische Simulation (INS)},
year = 2016,
month = mar,
INS Preprints},
volume = 1606,
note = {In this paper, an elliptic optimization problem with pointwise inequality constraints on the state is considered. The main contribution of this paper are a priori L2-error estimates for the discretization error in the optimal states. Due to the non separability of the space for the Lagrange multipliers for the inequality constraints, the problem is tackled by separation of the discretization error into two components. First, the state constraints are discretized. Second, with discretized inequality constraints, a duality argument for the error due to the discretization of the PDE is employed. For the second stage an a priori error estimate is derived with constants depending on the regularity of the dual problem. Finally, we discuss two cases in which these constants can be bounded in a favorable way; leading to higher order estimates than those induced by the known L2-error in the control variable. More precisely, we consider a given fixed number of pointwise inequality constraints and a case of infinitely many but only weakly active constraints.},
url = {https://hdl.handle.net/20.500.11811/11851}
}
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