Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simulation and Control of a Nonsmooth Cahn-Hilliard Navier-Stokes System   We are concerned with the simulation and control of a two phase flow model
governed by a coupled Cahn-Hilliard Navier-Stokes system involving a nonsmooth
energy potential. We establish the existence of optimal solutions and present
two distinct approaches to derive suitable stationarity conditions for the
bilevel problem, namely C- and strong stationarity. Moreover, we demonstrate
the numerical realization of these concepts at the hands of two adaptive
solution algorithms relying on a specifically developed goal-oriented error
estimator. In addition, we present a model order reduction approach using
proper orthogonal decomposition (POD-MOR) in order to replace high-fidelity
models by low order surrogates. In particular, we combine POD with
space-adapted snapshots and address the challenges which are the consideration
of snapshots with different spatial resolutions and the conservation of a
solenoidal property.

22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin