Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An a posteriori error analysis of an elliptic optimal control problem in
  measure space   We propose an a posteriori error estimator for a sparse optimal control
problem: the control variable lies in the space of regular Borel measures. We
consider a solution technique that relies on the discretization of the control
variable as a linear combination of Dirac measures. The proposed a posteriori
error estimator can be decomposed into the sum of two contributions: an error
estimator in the maximum norm for the discretization of the adjoint equation
and an estimator in the $L^2$-norm that accounts for the approximation of the
state equation. We prove that the designed error estimator is locally efficient
and we explore its reliability properties. The analysis is valid for two and
three-dimensional domains. We illustrate the theory with numerical examples.

12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph