A posteriori error estimation and adaptivity for elliptic optimal control problems with state constraints

In this paper optimal control problems governed by elliptic semilinear equations and subject to pointwise state constraints are considered. These problems are discretized using finite element methods and a posteriori error estimates are derived assessing the error with respect to the cost functional...

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Bibliographic Details
Published inComputational optimization and applications Vol. 44; no. 1; pp. 3 - 25
Main Authors Benedix, Olaf, Vexler, Boris
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.10.2009
Springer Nature B.V
Subjects
Control
Convex and Discrete Geometry
Error analysis
Finite element analysis
Inequality
Linear equations
Management Science
Mathematics
Mathematics and Statistics
Operations Research
Operations Research/Decision Theory
Optimization
Partial differential equations
Statistics
Studies
A posteriori error estimation
Finite elements
Semilinear equations
Optimal control
State constraints
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ISSN0926-6003
1573-2894
DOI10.1007/s10589-008-9200-y

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Summary:In this paper optimal control problems governed by elliptic semilinear equations and subject to pointwise state constraints are considered. These problems are discretized using finite element methods and a posteriori error estimates are derived assessing the error with respect to the cost functional. These estimates are used to obtain quantitative information on the discretization error as well as for guiding an adaptive algorithm for local mesh refinement. Numerical examples illustrate the behavior of the method.
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-008-9200-y