Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A posteriori error estimates for a distributed optimal control problem
  of the stationary Navier-Stokes equations   In two and three dimensional Lipschitz, but not necessarily convex, polytopal
domains, we propose and analyze a posteriori error estimators for an optimal
control problem involving the stationary Navier--Stokes equations; control
constraints are also considered. We devise two strategies of discretization: a
semi discrete scheme where the control variable is not discretized -- the
so-called variational discrezation approach -- and a fully discrete scheme
where the control is discretized with piecewise quadratic functions. For each
solution solution technique, we design an a posteriori error estimator that can
be decomposed as the sum of contributions related to the discretization of the
state and adjoint equations and, additionally, the discretization of the
control variable for when the fully discrete scheme is considered. We prove
that the devised error estimators are reliable and also explore local
efficiency estimates. Numerical experiments reveal a competitive performance of
adaptive loops based on the devised a posteriori error estimators.

23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph