Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adaptive FEM for parameter-errors in elliptic linear-quadratic parameter
  estimation problems   We consider an elliptic linear-quadratic parameter estimation problem with a
finite number of parameters. A novel a priori bound for the parameter error is
proved and, based on this bound, an adaptive finite element method driven by an
a posteriori error estimator is presented. Unlike prior results in the
literature, our estimator, which is composed of standard energy error residual
estimators for the state equation and suitable co-state problems, reflects the
faster convergence of the parameter error compared to the (co)-state variables.
We show optimal convergence rates of our method; in particular and unlike prior
works, we prove that the estimator decreases with a rate that is the sum of the
best approximation rates of the state and co-state variables. Experiments
confirm that our method matches the convergence rate of the parameter error.

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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
16
The categories of this paper are: stat