Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Goal oriented adaptivity in the IRGNM for parameter identification in
  PDEs II: all-at once formulations   In this paper we investigate adaptive discretization of the iteratively
regularized Gauss- Newton method IRGNM. All-at-once formulations considering
the PDE and the measurement equation simultaneously allow to avoid
(approximate) solution of a potentially nonlinear PDE in each Newton step as
compared to the reduced form [22]. We analyze a least squares and a generalized
Gauss-Newton formulation and in both cases prove convergence and convergence
rates with a posteriori choice of the regularization parameters in each Newton
step and of the stopping index under certain accuracy requirements on four
quantities of interest. Estimation of the error in these quantities by means of
a weighted dual residual method is discussed, which leads to an algorithm for
adaptive mesh refinement. Numerical experiments with an implementation of this
algorithm show the numerical efficiency of this approach, which especially for
strongly nonlinear PDEs outperforms the nonlinear Tikhonov regularization
considered in [21].

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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: bayes-an