Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiscale differential Riccati equations for linear quadratic regulator
  problems   We consider approximations to the solutions of differential Riccati equations
in the context of linear quadratic regulator problems, where the state equation
is governed by a multiscale operator. Similarly to elliptic and parabolic
problems, standard finite element discretizations perform poorly in this
setting unless the grid resolves the fine-scale features of the problem. This
results in unfeasible amounts of computation and high memory requirements. In
this paper, we demonstrate how the localized orthogonal decomposition method
may be used to acquire accurate results also for coarse discretizations, at the
low cost of solving a series of small, localized elliptic problems. We prove
second-order convergence (except for a logarithmic factor) in the $L^2$
operator norm, and first-order convergence in the corresponding energy norm.
These results are both independent of the multiscale variations in the state
equation. In addition, we provide a detailed derivation of the fully discrete
matrix-valued equations, and show how they can be handled in a low-rank setting
for large-scale computations. In connection to this, we also show how to
efficiently compute the relevant operator-norm errors. Finally, our theoretical
results are validated by several numerical experiments.

23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin