Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the convergence of second-order in time numerical discretizations for
  the evolution Navier-Stokes equations   We prove the convergence of certain second-order numerical methods to weak
solutions of the Navier-Stokes equations satisfying in addition the local
energy inequality, and therefore suitable in the sense of Scheffer and
Caffarelli-Kohn-Nirenberg. More precisely, we treat the space-periodic case in
three space-dimensions and we consider a full discretization in which the the
classical Crank-Nicolson method ($\theta$-method with $\theta=1/2$) is used to
discretize the time variable, while in the space variables we consider finite
elements. The convective term is discretized in several implicit,
semi-implicit, and explicit ways. In particular, we focus on proving (possibly
conditional) convergence of the discrete solutions towards weak solutions
(satisfying a precise local energy balance), without extra regularity
assumptions on the limit problem. We do not prove orders of convergence, but
our analysis identifies some numerical schemes providing also alternate proofs
of existence of "physically relevant" solutions in three space dimensions.

12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga