Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Mixed Finite Element Approximation for Fluid Flows of Mixed Regimes in
  Porous Media   In this paper, we consider the complex flows when all three regimes
pre-Darcy, Darcy and post-Darcy may be present in different portions of a same
domain. We unify all three flow regimes under mathematics formulation. We
describe the flow of a single-phase fluid in $\R^d, d\ge 2$ by a nonlinear
degenerate system of density and momentum. A mixed finite element method is
proposed for the approximation of the solution of the above system. The
stability of the approximations are proved; the error estimates are derived for
the numerical approximations for both continuous and discrete time procedures.
The continuous dependence of numerical solutions on physical parameters are
demonstrated. Experimental studies are presented regarding convergence rates
and showing the dependence of the solution on the physical parameters.

9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ