2005
DOI: 10.1007/s10589-005-2180-2
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Error Estimates for the Numerical Approximation of Boundary Semilinear Elliptic Control Problems

Abstract: We study the numerical approximation of boundary optimal control problems governed by semilinear elliptic partial differential equations with pointwise constraints on the control. The analysis of the approximate control problems is carried out. The uniform convergence of discretized controls to optimal controls is proven under natural assumptions by taking piecewise constant controls. Finally, error estimates are established. Abstract. We study the numerical approximation of boundary optimal control problems g… Show more

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Cited by 121 publications
(127 citation statements)
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“…The proof of this lemma follows the steps of [6,Lemma 4.8]. Indeed,λ does not play any role in the proof.…”
Section: Error Estimatesmentioning
confidence: 98%
“…The proof of this lemma follows the steps of [6,Lemma 4.8]. Indeed,λ does not play any role in the proof.…”
Section: Error Estimatesmentioning
confidence: 98%
“…For instance, it was used by Malanowski et al [21] in the context of error estimates for the optimal control of ODEs. It was extended later to elliptic optimal control problems in [1] and [5]. Let us explain this basic idea here.…”
Section: A-posteriori Error Analysismentioning
confidence: 99%
“…We summarize them, as well as some of their immediate consequences in the following lemmas. For detailed proofs we refer to [5,7]. For every u ∈ U ad , we define the adjoint state associated with u as the unique solution to equation…”
Section: First Order Optimality Conditionsmentioning
confidence: 99%
“…The space of discretized controls is We denote the solutions of problem (P h ) and (P h ε ) byū h andū h ε respectively. We address the reader to [7] for the details about the optimization process, [4] for theory about continuous piecewise linear approximation of Neumann control problems, and [5] for theory about approximation of Dirichlet control problems.…”
Section: An Examplementioning
confidence: 99%