Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis of a Mixed Finite Element Method for a
  Cahn-Hilliard-Darcy-Stokes System   In this paper we devise and analyze a mixed finite element method for a
modified Cahn-Hilliard equation coupled with a non-steady Darcy-Stokes flow
that models phase separation and coupled fluid flow in immiscible binary fluids
and diblock copolymer melts. The time discretization is based on a convex
splitting of the energy of the equation. We prove that our scheme is
unconditionally energy stable with respect to a spatially discrete analogue of
the continuous free energy of the system and unconditionally uniquely solvable.
We prove that the phase variable is bounded in $L^\infty
\left(0,T,L^\infty\right)$ and the chemical potential is bounded in $L^\infty
\left(0,T,L^2\right)$ absolutely unconditionally in two and three dimensions,
for any finite final time $T$. We subsequently prove that these variables
converge with optimal rates in the appropriate energy norms in both two and
three dimensions.

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The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas