Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A posteriori error estimates for an optimal control problem with a
  bilinear state equation   We propose and analyze a posteriori error estimators for an optimal control
problem that involves an elliptic partial differential equation as state
equation and a control variable that enters the state equation as a
coefficient; pointwise constraints on the control variable are considered as
well. We consider two different strategies to approximate optimal variables: a
fully discrete scheme in which the admissible control set is discretized with
piecewise constant functions and a semi-discrete scheme where the admissible
control set is not discretized; the latter scheme being based on the so-called
variational discretization approach. We design, for each solution technique, an
a posteriori error estimator and show, in two and three dimensional Lipschitz
polygonal/polyhedral domains (not necessarily convex), that the proposed error
estimator is reliable and efficient. We design, based on the devised
estimators, adaptive strategies that deliver optimal experimental rates of
convergence for the performed numerical examples.

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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas