Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite element error analysis for measure-valued optimal control
  problems governed by a 1D wave equation with variable coefficients   This work is concerned with the optimal control problems governed by a 1D
wave equation with variable coefficients and the control spaces $\mathcal M_T$
of either measure-valued functions $L_{w^*}^2(I,\mathcal M(\Omega))$ or vector
measures $\mathcal M(\Omega,L^2(I))$. The cost functional involves the standard
quadratic tracking terms and the regularization term $\alpha\|u\|_{\mathcal
M_T}$ with $\alpha>0$. We construct and study three-level in time bilinear
finite element discretizations for this class of problems. The main focus lies
on the derivation of error estimates for the optimal state variable and the
error measured in the cost functional. The analysis is mainly based on some
previous results of the authors. The numerical results are included.

16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
3
The categories of this paper are: physics