Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Robust discretization and solvers for elliptic optimal control problems
  with energy regularization   We consider the finite element discretization and the iterative solution of
singularly perturbed elliptic reaction-diffusion equations in three-dimensional
computational domains. These equations arise from the optimality conditions for
elliptic distributed optimal control problems with energy regularization that
were recently studied by M.~Neum\"{u}ller and O.~Steinbach (2020). We provide
quasi-optimal a priori finite element error estimates which depend both on the
mesh size $h$ and on the regularization parameter $\varrho$. The choice
$\varrho = h^2$ ensures optimal convergence which only depends on the
regularity of the target function. For the iterative solution, we employ an
algebraic multigrid preconditioner and a balancing domain decomposition by
constraints (BDDC) preconditioner. We numerically study robustness and
efficiency of the proposed algebraic preconditioners with respect to the mesh
size $h$, the regularization parameter $\varrho$, and the number of subdomains
(cores) $p$. Furthermore, we investigate the parallel performance of the BDDC
preconditioned conjugate gradient solver.

12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin